**"****Local Structure
of Groups and of Their Classifying Spaces****"**

By

**(Université
PARIS 13)
**

** Abstract:** This
will be a survey talk on the close relationship between the local structure of
a finite group or compact Lie group and that of its classifying space. By
the ``p-local structure'' of a group G, for a prime p, is meant the structure
of a Sylow p-subgroup S of G (a maximal p-toral subgroup if G is compact Lie), together with all G-conjugacy relations between elements and subgroups of
S. By the p-local structure of the classifying space BG is meant the
structure (homotopy properties) of the p-completion
of BG. For example, by a conjecture of Martino and Priddy,
now a theorem, two finite groups G and H have equivalent p-local structures if
and only if the p-completions of BG and BH are homotopy
equivalent. This (the ``if'' part of the statement) was used, in joint work
with Broto and M{\o}ller, to prove
a general theorem about local equivalences between finite Lie groups --- a
result for which no purely algebraic proof is known. As another example, these
ideas have allowed us to extend the family of p-completed classifying spaces of
(finite or compact Lie) groups to a much larger family of spaces which have
many of the same very nice homotopy theoretic
properties.

**Date: ****Wednesday, April 16, 2014**

**Time: ****15.40 – 16:30 **

**Place: ****Mathematics Seminar Room, SA-141**

Tea and cookies will be served after the
seminar.