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Contribution Invited speaker

Topologie algébrique et applications

Local structure of finite groups and their p-completed classifying spaces

Intervenant(s)

  • Prof. Bob OLIVER

Auteurs principaux

Content

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.