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# Barcelona Algebraic Topology Group

Barcelona Algebraic Topology Group
 Friday's Topology Seminar 2016-2017
 Date and Place: February 17th 12h, seminar room C3b/158Speaker: Mitsunobu Tsutaya (Kyushu University)Title: Infiniteness of $A_\infty$-types of gauge groupsAbstract: 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. See the calendar for upcoming events. Read more...

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