Orateur
Prof.
Bob Oliver
Description
I plan to describe the close connection between the homotopy theoretic
properties of the $p$-completed classifying space of a finite group $G$ and
the $p$-local group theoretic properties of $G$. One way in which this
arises is in the following theorem originally conjectured by Martino and
Priddy: for finite groups $G$ and $H$, $BG{}^\wedge_p\simeq BH{}^\wedge_p$ if and only
if $G$ and $H$ have the same $p$-local structure (the same conjugacy
relations among $p$-subgroups). Another involves a description, in terms of
the $p$-local properties of $G$, of the group $\mathrm{Out}(BG{}^\wedge_p)$ of homotopy
classes of self equivalences of $BG{}^\wedge_p$.
After describing the general results, I'll give some examples and
applications of both of these, especially in the case where $G$ and $H$ are
simple Lie groups over finite fields.
Auteur principal
Prof.
Bob Oliver
(Université Paris 13)
