Mark Feshbach
 	       University of Minnesota

How to split a classifying space of a finite group

Abstract: The proof of the Segal Conjecture has had many
consequences. One of them is an algebraic model for the space of
stable maps from the classifying space of a finite group to that of
another. This in particular allows one to split classifying spaces
into indecomposable pieces. Representation theory plays a large role
in this, as does subgroup structure. Although the final answer is
quite complicated the general picture is quite pleasing. Some of these
ideas can be generalized to compact Lie groups.