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Relative self-equivalences and graph complexes
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.ORCID-id: 0000-0002-2068-6228
2024 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis consists of three papers.

In Paper I, we identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of Sk × Sl, where 3 ≤ k < l ≤ 2k - 2. We express the result in terms of Lie graph complex homology.

In Paper II, we construct a rational model for the classifying space BautA(X) of homotopy automorphisms of a simply connected finite CW-complex X relative to a simply connected subcomplex A. Using this model, we provide a purely algebraic description of the cohomology of this classifying space. This constitutes an important input for the results of Paper I.

In Paper III, we show that modular operads are equivalent to modules over a certain simple properad which we call the Brauer properad. Furthermore we show that the Feynman transform corresponds to the cobar construction for modules of this kind. To make this precise, we extend the machinery of the bar and cobar constructions relative to a twisting morphism to modules over a general properad. As an application, we provide the foundations of a Koszul duality theory for modular operads.

sted, utgiver, år, opplag, sider
Stockholm: Department of Mathematics, Stockholm University , 2024. , s. xxix
HSV kategori
Forskningsprogram
matematik
Identifikatorer
URN: urn:nbn:se:su:diva-228529ISBN: 978-91-8014-793-4 (tryckt)ISBN: 978-91-8014-794-1 (digital)OAI: oai:DiVA.org:su-228529DiVA, id: diva2:1853120
Disputas
2024-06-13, Lärosal 4, hus 1, Albano, Albanovägen 28, Stockholm, 14:00 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2024-05-21 Laget: 2024-04-21 Sist oppdatert: 2024-04-29bibliografisk kontrollert
Delarbeid
1. The stable cohomology of self-equivalences of connected sums of products of spheres
Åpne denne publikasjonen i ny fane eller vindu >>The stable cohomology of self-equivalences of connected sums of products of spheres
2024 (engelsk)Inngår i: Forum of mathematics, sigma, ISSN 2050-5094, Vol. 12, artikkel-id e1Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of Sk×Sl, where 3≤k<l2k−2. The result is expressed in terms of Lie graph complex homology.

HSV kategori
Identifikatorer
urn:nbn:se:su:diva-226075 (URN)10.1017/fms.2023.113 (DOI)001136559700001 ()
Tilgjengelig fra: 2024-02-01 Laget: 2024-02-01 Sist oppdatert: 2024-04-21bibliografisk kontrollert
2. Equivariant algebraic models for relative self-equivalences
Åpne denne publikasjonen i ny fane eller vindu >>Equivariant algebraic models for relative self-equivalences
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-228528 (URN)
Tilgjengelig fra: 2024-04-21 Laget: 2024-04-21 Sist oppdatert: 2024-04-21
3. MODULAR OPERADS AS MODULES OVER THE BRAUER PROPERAD
Åpne denne publikasjonen i ny fane eller vindu >>MODULAR OPERADS AS MODULES OVER THE BRAUER PROPERAD
2022 (engelsk)Inngår i: Theory and Applications of Categories, ISSN 1201-561X, Vol. 38, nr 40, s. 1538-1607Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We show that modular operads are equivalent to modules over a certain simple properad which we call the Brauer properad. Furthermore, we show that, in this setting, the Feynman transform corresponds to the cobar construction for modules of this kind. To make this precise, we extend the machinery of the bar and cobar constructions relative to a twisting morphism to modules over a general properad. This generalizes the classical case of algebras over an operad and might be of independent interest. As an application, we sketch a Koszul duality theory for modular operads.

Emneord
Modular operads, properads, Koszul duality
HSV kategori
Identifikatorer
urn:nbn:se:su:diva-214565 (URN)000904058600001 ()
Tilgjengelig fra: 2023-02-06 Laget: 2023-02-06 Sist oppdatert: 2024-04-21bibliografisk kontrollert

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Relative self-equivalences and graph complexes(711 kB)63 nedlastinger
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