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The stable cohomology of self-equivalences of connected sums of products of spheres
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-2068-6228
Number of Authors: 12024 (English)In: Forum of mathematics, sigma, ISSN 2050-5094, Vol. 12, article id e1Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
2024. Vol. 12, article id e1
National Category
Geometry
Identifiers
URN: urn:nbn:se:su:diva-226075DOI: 10.1017/fms.2023.113ISI: 001136559700001OAI: oai:DiVA.org:su-226075DiVA, id: diva2:1833483
Available from: 2024-02-01 Created: 2024-02-01 Last updated: 2024-04-21Bibliographically approved
In thesis
1. Relative self-equivalences and graph complexes
Open this publication in new window or tab >>Relative self-equivalences and graph complexes
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
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.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2024. p. xxix
National Category
Geometry
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-228529 (URN)978-91-8014-793-4 (ISBN)978-91-8014-794-1 (ISBN)
Public defence
2024-06-13, Lärosal 4, hus 1, Albano, Albanovägen 28, Stockholm, 14:00 (English)
Opponent
Supervisors
Available from: 2024-05-21 Created: 2024-04-21 Last updated: 2024-04-29Bibliographically approved

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Stoll, Robin

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