Department of Mathematics

## BÝLKENT TOPOLOGY SEMINAR

"Automorphisms and Extensions of Fusion Systems"

By

BOB OLIVER
(Université Paris 13)

Abstract: Fix a prime $p$. A fusion system $\mathcal{F}$ is \emph{tamely realized} by a finite group $G$ if $\mathcal{F}\cong\mathcal{F}_S(G)$ (for $S\in\textup{Syll_p(G)$) and the natural map from $\textup{Out}(G)$ to $\textup{Out}(BG^\wedge_p)$ is split surjective. Here, $\textup{Out}(X)$(for a space $X$) means the group of homotopy classes of self homotopy equivalences, and $BG^\wedge_p$ is the $p$-completion of the classifying space of $G$. We say that a fusion system $\mathcal{F}$ is \emph{tame} if it is tamely realized by some finite group.

Tameness plays an important role when studying extensions of fusion systems, and through that when using fusion systems to classify certain classes of finite groups. It is also interesting in its own right as a means of describing self equivalences of the space $BG^\wedge_p$ in terms of $\textup{Out}(G)$. The goal of this talk is to explain these connections, and also to describe recent progress in proving tameness forfusion systems of  finite simple groups.


Date:  Monday, May 2, 2016

Time: 13.40-14.30

Place: Mathematics Seminar Room, SA-141

All are most cordially invited. Tea and cookies will be served after the talk.