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Barcelona Algebraic Topology Group

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Barcelona Algebraic Topology Group
Friday's Topology Seminar 2016-2017 PDF Print E-mail

Date and Place: February 17th 12h, seminar room C3b/158
Speaker:
Mitsunobu Tsutaya (Kyushu University)
Title:
Infiniteness of $A_\infty$-types of gauge groups

Abstract:
Let $G$ be a compact connected Lie group and $B$ be a finite CW complex. The gauge group of a principal $G$-bundle $P\to B$ is the (typically infinite dimensional) group of automorphisms. The problem we consider is how many $A_n$-equivalence classes appear among the gauge groups of the principal bundles for fixed $G$ and $B$, where the $A_n$-equivalence is in the sense of Stasheff. Crabb-Sutherland and the speaker proved that the number of the $A_n$-equivalence classes of the gauge groups is finite if $n<\infty$. The main theorem of this talk states that this finiteness typically breaks down if $B$ is an appropriate sphere and $n=\infty$. In the proof, the theory of unstable algebras plays an important role. This talk is based on a joint work with Daisuke Kishimoto.

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Presentation

This is the web site of the Algebraic Topology Team in Barcelona (Grup de Topologia Algebraica de Barcelona, 2014SGR-42 and Homotopy theory of algebraic structures, MTM2016-80439-P).

Our research interests include a variety of subjects in algebraic topology, group theory, homological algebra, and category theory. Here you will find information about us and our common activities.

 

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