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1. Characteristic classes for families of bundles Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt606",{id:"formSmash:items:resultList:0:j_idt606",widgetVar:"widget_formSmash_items_resultList_0_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Characteristic classes for families of bundles2022In: Selecta Mathematica, New Series, ISSN 1022-1824, E-ISSN 1420-9020, Vol. 28, no 3, article id 51Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:0:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_0_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The generalized Miller–Morita–Mumford classes of a manifold bundle with fiber

*M*depend only on the underlying*τM-fibration*, meaning the family of vector bundles formed by the tangent bundles of the fibers. This motivates a closer study of the classifying space for*τM*-fibrations,*Baut(τM)*, and its cohomology ring, i.e., the ring of characteristic classes of*τM*-fibrations. For a bundle*ξ*over a simply connected Poincaré duality space, we construct a relative Sullivan model for the universal*ξ*-fibration with holonomy in a given connected monoid, together with explicit cocycle representatives for the characteristic classes of the canonical bundle over its total space. This yields tools for computing the rational cohomology ring of*Baut(ξ)*as well as the subring generated by the generalized Miller–Morita–Mumford classes. To illustrate, we carry out sample computations for spheres and complex projective spaces. We discuss applications to tautological rings of simply connected manifolds and to the problem of deciding whether a given*τM*-fibration comes from a manifold bundle.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:0:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 2. Cofinite Hochschild cohomology Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt606",{id:"formSmash:items:resultList:1:j_idt606",widgetVar:"widget_formSmash_items_resultList_1_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics. Matematik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Cofinite Hochschild cohomology2007Report (Other academic)3. Homological perturbation theory for algebras over operads Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt606",{id:"formSmash:items:resultList:2:j_idt606",widgetVar:"widget_formSmash_items_resultList_2_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homological perturbation theory for algebras over operads2014In: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 14, no 5, p. 2511-2548Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:2:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_2_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O . To solve this problem, we introduce thick maps of O –algebras and special thick maps that we call pseudo-derivations that serve as appropriate generalizations of algebra homotopies for the purposes of homological perturbation theory.

As an application, we derive explicit formulas for transferring Ω(C) –algebra structures along contractions, where C is any connected cooperad in chain complexes. This specializes to transfer formulas for O ∞ –algebras for any Koszul operad O , in particular for A ∞ –, C ∞ –, L ∞ – and G ∞ –algebras. A key feature is that our formulas are expressed in terms of the compact description of Ω(C) –algebras as coderivation differentials on cofree C –coalgebras. Moreover, we get formulas not only for the transferred structure and a structure on the inclusion, but also for structures on the projection and the homotopy

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:2:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 4. Poincaré series and homotopy Lie algebras of monomial rings Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt606",{id:"formSmash:items:resultList:3:j_idt606",widgetVar:"widget_formSmash_items_resultList_3_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics. Matematik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Poincaré series and homotopy Lie algebras of monomial rings2005Licentiate thesis, monograph (Other academic)5. Poincaré series of monomial rings Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt606",{id:"formSmash:items:resultList:4:j_idt606",widgetVar:"widget_formSmash_items_resultList_4_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics. Matematik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Poincaré series of monomial rings2006In: Journal of Algebra, Vol. 295, no 1, p. 211-230Article in journal (Refereed)6. Rational homotopy theory of mapping spaces via Lie theory for L-infinity algebras Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt606",{id:"formSmash:items:resultList:5:j_idt606",widgetVar:"widget_formSmash_items_resultList_5_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Rational homotopy theory of mapping spaces via Lie theory for L-infinity algebras2015In: Homology, Homotopy and Applications, ISSN 1532-0073, E-ISSN 1532-0081, Vol. 17, no 2, p. 343-369Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:5:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_5_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We calculate the higher homotopy groups of the Deligne–Getzler ∞-groupoid associated to a nilpotent L∞-algebra. As an application, we present a new approach to the rational homotopy theory of mapping spaces.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:5:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 7. Rational Models for Automorphisms of Fiber Bundles Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt606",{id:"formSmash:items:resultList:6:j_idt606",widgetVar:"widget_formSmash_items_resultList_6_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Rational Models for Automorphisms of Fiber Bundles2020In: Documenta Mathematica, ISSN 1431-0635, E-ISSN 1431-0643, Vol. 25, p. 239-265Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:6:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_6_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Given a fiber bundle, we construct a differential graded Lie algebra model, in the sense of Quillen's rational homotopy theory, for the classifying space of the monoid of homotopy equivalences of the base covered by a fiberwise isomorphism of the total space.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:6:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 8. Shellability and the strong gcd-condition Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt606",{id:"formSmash:items:resultList:7:j_idt606",widgetVar:"widget_formSmash_items_resultList_7_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Shellability and the strong gcd-condition2009In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 16, no 2Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:7:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_7_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Shellability is a well-known combinatorial criterion on a simplicial complex for verifying that the associated Stanley-Reisner ring k[] is Cohen-Macaulay. Anotion familiar to commutative algebraists, but which has not received as muchattention from combinatorialists as the Cohen-Macaulay property, is the notion ofa Golod ring. Recently, J¨ollenbeck introduced a criterion on simplicial complexesreminiscent of shellability, called the strong gcd-condition, and he together with theauthor proved that it implies Golodness of the associated Stanley-Reisner ring. Thetwo algebraic notions were earlier tied together by Herzog, Reiner and Welker, whoshowed that if k[∨] is sequentially Cohen-Macaulay, where ∨ is the Alexanderdual of , then k[] is Golod. In this paper, we present a combinatorial companionof this result, namely that if ∨ is (non-pure) shellable then satisfies the stronggcd-condition. Moreover, we show that all implications just mentioned are strict ingeneral but that they are equivalences if is a flag complex.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:7:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 9. Shellability and the strong gcd-condition Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt606",{id:"formSmash:items:resultList:8:j_idt606",widgetVar:"widget_formSmash_items_resultList_8_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Shellability and the strong gcd-condition2009In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 16, no 2Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:8:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_8_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Shellability is a well-known combinatorial criterion on a simplicial complex for verifying that the associated Stanley-Reisner ring k[] is Cohen-Macaulay. Anotion familiar to commutative algebraists, but which has not received as muchattention from combinatorialists as the Cohen-Macaulay property, is the notion ofa Golod ring. Recently, J¨ollenbeck introduced a criterion on simplicial complexesreminiscent of shellability, called the strong gcd-condition, and he together with theauthor proved that it implies Golodness of the associated Stanley-Reisner ring. Thetwo algebraic notions were earlier tied together by Herzog, Reiner and Welker, whoshowed that if k[∨] is sequentially Cohen-Macaulay, where ∨ is the Alexanderdual of , then k[] is Golod. In this paper, we present a combinatorial companionof this result, namely that if ∨ is (non-pure) shellable then satisfies the stronggcd-condition. Moreover, we show that all implications just mentioned are strict ingeneral but that they are equivalences if is a flag complex.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 10. Hirzebruch L-polynomials and multiple zeta values Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt606",{id:"formSmash:items:resultList:9:j_idt606",widgetVar:"widget_formSmash_items_resultList_9_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt609",{id:"formSmash:items:resultList:9:j_idt609",widgetVar:"widget_formSmash_items_resultList_9_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Bergström, JonasStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hirzebruch L-polynomials and multiple zeta values2018In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 372, no 1-2, p. 125-137Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:9:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_9_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We express the coefficients of the Hirzebruch L-polynomials in terms of certain alternating multiple zeta values. In particular, we show that every monomial in the Pontryagin classes appears with a non-zero coefficient, with the expected sign. Similar results hold for the polynomials associated to the Â-genus.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Combinatorics of multigraded Poincaré series for monomial rings Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt606",{id:"formSmash:items:resultList:10:j_idt606",widgetVar:"widget_formSmash_items_resultList_10_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt609",{id:"formSmash:items:resultList:10:j_idt609",widgetVar:"widget_formSmash_items_resultList_10_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics. Matematik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Blasiak, JonahHersh, PatriciaPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Combinatorics of multigraded Poincaré series for monomial rings2007In: Journal of Algebra, Vol. 308, no 1, p. 73-90Article in journal (Refereed)12. Free loop space homology of highly connected manifolds Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt606",{id:"formSmash:items:resultList:11:j_idt606",widgetVar:"widget_formSmash_items_resultList_11_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt609",{id:"formSmash:items:resultList:11:j_idt609",widgetVar:"widget_formSmash_items_resultList_11_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Börjeson, KajStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Free loop space homology of highly connected manifolds2017In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 29, no 1, p. 201-228Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:11:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_11_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We calculate the homology of the free loop space of (n - 1)-connected closed manifolds of dimension at most 3 n - 2 (n >= 2), with the Chas-Sullivan loop product and loop bracket. Over a field of characteristic zero, we obtain an expression for the BV-operator. We also give explicit formulas for the Betti numbers, showing they grow exponentially. Our main tool is the connection between formality, coformality and Koszul algebras that was elucidated by the first author [6].

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:11:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 13. Koszul A<sub>∞</sub>-algebras and free loop space homology Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt606",{id:"formSmash:items:resultList:12:j_idt606",widgetVar:"widget_formSmash_items_resultList_12_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt609",{id:"formSmash:items:resultList:12:j_idt609",widgetVar:"widget_formSmash_items_resultList_12_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Börjeson, KajStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Koszul A_{∞}-algebras and free loop space homologyManuscript (preprint) (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:12:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_12_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We introduce a notion of Koszul A

_{∞}-algebra that generalizes Priddy’s notion of a Koszul algebra and we use it to construct small A_{∞}- algebra models for Hochschild cochains. As an application, this yields new techniques for computing free loop space homology algebras of manifolds that are either formal or coformal (over a field or over the integers). We illustrate these techniques in two examples.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:12:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 14. Koszul A(infinity)-algebras and free loop space homology Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt606",{id:"formSmash:items:resultList:13:j_idt606",widgetVar:"widget_formSmash_items_resultList_13_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt609",{id:"formSmash:items:resultList:13:j_idt609",widgetVar:"widget_formSmash_items_resultList_13_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Börjeson, KajPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Koszul A(infinity)-algebras and free loop space homology2020In: Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, E-ISSN 1464-3839, Vol. 63, no 1, p. 37-65Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:13:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_13_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We introduce a notion of Koszul A(infinity)-algebra that generalizes Priddy's notion of a Koszul algebra and we use it to construct small A(infinity)-algebra models for Hochschild cochains. As an application, this yields new techniques for computing free loop space homology algebras of manifolds that are either formal or coformal (over a field or over the integers). We illustrate these techniques in two examples.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:13:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 15. Homotopic Hopf-Galois extensions revisited Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt606",{id:"formSmash:items:resultList:14:j_idt606",widgetVar:"widget_formSmash_items_resultList_14_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt609",{id:"formSmash:items:resultList:14:j_idt609",widgetVar:"widget_formSmash_items_resultList_14_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hess, KathrynPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homotopic Hopf-Galois extensions revisitedManuscript (preprint) (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:14:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_14_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this article we revisit the theory of homotopic Hopf-Galois extensions introduced in arXiv:0902.3393v2 [math.AT], in light of the homotopical Morita theory of comodules established in arXiv:1411.6517 [math.AT]. We generalize the theory to a relative framework, which we believe is new even in the classical context and which is essential for treating the Hopf-Galois correspondence in forthcoming work of the second author and Karpova. We study in detail homotopic Hopf-Galois extensions of differential graded algebras over a commutative ring, for which we establish a descent-type characterization analogous to the one Rognes provided in the context of ring spectra. An interesting feature in the differential graded setting is the close relationship between homotopic Hopf-Galois theory and Koszul duality theory. We show that nice enough principal fibrations of simplicial sets give rise to homotopic Hopf-Galois extensions in the differential graded setting, for which this Koszul duality has a familiar form.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:14:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 16. Homotopic Hopf-Galois extensions revisited Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt606",{id:"formSmash:items:resultList:15:j_idt606",widgetVar:"widget_formSmash_items_resultList_15_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt609",{id:"formSmash:items:resultList:15:j_idt609",widgetVar:"widget_formSmash_items_resultList_15_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hess, KathrynPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homotopic Hopf-Galois extensions revisited2018In: Journal of Noncommutative Geometry, ISSN 1661-6952, E-ISSN 1661-6960, Vol. 12, no 1, p. 107-155Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:15:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_15_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this article we revisit the theory of homotopic Hopf-Galois extensions introduced in [9], in light of the homotopical Morita theory of comodules established in [3]. We generalize the theory to a relative framework, which we believe is new even in the classical context and which is essential for treating the Hopf-Galois correspondence in [19]. We study in detail homotopic Hopf-Galois extensions of differential graded algebras over a commutative ring, for which we establish a descent-type characterization analogous to the one Rognes provided in the context of ring spectra [26]. An interesting feature in the differential graded setting is the close relationship between homotopic Hopf-Galois theory and Koszul duality theory. We show that nice enough principal fibrations of simplicial sets give rise to homotopic Hopf-Galois extensions in the differential graded setting, for which this Koszul duality has a familiar form.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:15:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 17. Homotopical Morita theory for corings Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt606",{id:"formSmash:items:resultList:16:j_idt606",widgetVar:"widget_formSmash_items_resultList_16_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt609",{id:"formSmash:items:resultList:16:j_idt609",widgetVar:"widget_formSmash_items_resultList_16_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hess, KathrynPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homotopical Morita theory for coringsManuscript (preprint) (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:16:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_16_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A coring (A,C) consists of an algebra A and a coalgebra C in the monoidal category of A-bimodules. Corings and their comodules arise naturally in the study of Hopf-Galois extensions and descent theory, as well as in the study of Hopf algebroids. In this paper, we address the question of when two corings in a symmetric monoidal model category V are homotopically Morita equivalent, i.e., when their respective categories of comodules are Quillen equivalent. The category of comodules over the trivial coring (A,A) is isomorphic to the category of A-modules, so the question above englobes that of when two algebras are homotopically Morita equivalent. We discuss this special case in the first part of the paper, extending previously known results. To approach the general question, we introduce the notion of a 'braided bimodule' and show that adjunctions between A-Mod and B-Mod that lift to adjunctions between (A,C)-Comod and (B,D)-Comod correspond precisely to braided bimodules between (A,C) and (B,D). We then give criteria, in terms of homotopic descent, for when a braided bimodule induces a Quillen equivalence. In particular, we obtain criteria for when a morphism of corings induces a Quillen equivalence, providing a homotopic generalization of results by Hovey and Strickland on Morita equivalences of Hopf algebroids. To illustrate the general theory, we examine homotopical Morita theory for corings in the category of chain complexes over a commutative ring.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:16:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 18. Homotopical Morita theory for corings Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt606",{id:"formSmash:items:resultList:17:j_idt606",widgetVar:"widget_formSmash_items_resultList_17_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt609",{id:"formSmash:items:resultList:17:j_idt609",widgetVar:"widget_formSmash_items_resultList_17_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hess, KathrynPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homotopical Morita theory for corings2018In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 227, no 1, p. 239-287Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:17:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_17_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A coring (A,C) consists of an algebra A in a symmetric monoidal category and a coalgebra C in the monoidal category of A-bimodules. Corings and their comodules arise naturally in the study of Hopf-Galois extensions and descent theory, as well as in the study of Hopf algebroids. In this paper, we address the question of when two corings (A,C) and (B,D) in a symmetric monoidal model category V are homotopically Morita equivalent, i.e., when their respective categories of comodules V (C)(A) and V (D)(B) are Quillen equivalent. As an illustration of the general theory, we examine homotopical Morita theory for corings in the category of chain complexes over a commutative ring.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:17:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 19. On the Golod property of Stanley-Reisner rings Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt606",{id:"formSmash:items:resultList:18:j_idt606",widgetVar:"widget_formSmash_items_resultList_18_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt609",{id:"formSmash:items:resultList:18:j_idt609",widgetVar:"widget_formSmash_items_resultList_18_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics. Matematik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Jöllenbeck, MichaelPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On the Golod property of Stanley-Reisner rings2007In: Journal of Algebra, Vol. 315, no 1, p. 249-273Article in journal (Refereed)20. Rational homotopy theory of automorphisms of highly connected manifolds Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt606",{id:"formSmash:items:resultList:19:j_idt606",widgetVar:"widget_formSmash_items_resultList_19_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt609",{id:"formSmash:items:resultList:19:j_idt609",widgetVar:"widget_formSmash_items_resultList_19_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Madsen, IbPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Rational homotopy theory of automorphisms of highly connected manifoldsManuscript (preprint) (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:19:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_19_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study the rational homotopy types of classifying spaces of automorphism groups of 2d-dimensional (d-1)-connected manifolds (d > 2). We prove that the rational homology groups of the homotopy automorphisms and the block diffeomorphisms of the manifold #^g S^d x S^d relative to a disk stabilize as g increases. Via a theorem of Kontsevich, we obtain the striking result that the stable rational cohomology of the homotopy automorphisms comprises all unstable rational homology groups of all outer automorphism groups of free groups.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:19:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 21. Rational homotopy theory of automorphisms of manifolds Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt606",{id:"formSmash:items:resultList:20:j_idt606",widgetVar:"widget_formSmash_items_resultList_20_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt609",{id:"formSmash:items:resultList:20:j_idt609",widgetVar:"widget_formSmash_items_resultList_20_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Madsen, IbPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Rational homotopy theory of automorphisms of manifolds2020In: Acta Mathematica, ISSN 0001-5962, E-ISSN 1871-2509, Vol. 224, no 1, p. 67-185Article in journal (Refereed)22. A dg Lie model for relative homotopy automorphisms Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt606",{id:"formSmash:items:resultList:21:j_idt606",widgetVar:"widget_formSmash_items_resultList_21_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt609",{id:"formSmash:items:resultList:21:j_idt609",widgetVar:"widget_formSmash_items_resultList_21_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Saleh, BasharStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A dg Lie model for relative homotopy automorphisms2020In: Homology, Homotopy and Applications, ISSN 1532-0073, E-ISSN 1532-0081, Vol. 22, no 2, p. 105-121Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:21:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_21_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We construct a dg" role="presentation" style="display: inline; line-height: normal; font-size: 17.3333px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(64, 64, 64); font-family: "Times New Roman", Times, serif; position: relative;">dgdg Lie algebra model for the universal cover of the classifying space of the grouplike monoid of homotopy automorphisms of a space that fix a given subspace. We derive the model from a known model for based homotopy automorphisms together with general result on rational models for geometric bar constructions.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:21:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 23. Equivariant algebraic models for relative self-equivalences Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt606",{id:"formSmash:items:resultList:22:j_idt606",widgetVar:"widget_formSmash_items_resultList_22_j_idt606",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt609",{id:"formSmash:items:resultList:22:j_idt609",widgetVar:"widget_formSmash_items_resultList_22_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Stoll, RobinStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Equivariant algebraic models for relative self-equivalencesManuscript (preprint) (Other academic)

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