TOPOLOGY SEMINAR

**"****Saturated
Fusion Systems as Stable Reacts of Groups****"**

**Abstract: ****A saturated fusion system
associated to a finite group G encodes the p-structure of the group as the
Sylow p-subgroup enriched with additional
conjugation. The fusion system contains just the
right amount of algebraic information to for instance reconstruct the p-completion of
BG, but not BG itself. Abstract saturated fusion systems F without ambient
groups exist, and these have (p-completed) classifying spaces BF as well.
In spectra, the suspension spectrum of BF becomes a
retract of the suspension spectrum of BS, for the Sylow
p-subgroup S, so BF gets encoded as a characteristic idempotent in the
double Burnside ring of S. This way of looking as fusion systems as stable
retracts of their Sylow p-subgroups is a very useful
tool for generalizing theorems from groups or p-groups to saturated fusion
systems. In joint work with Tomer Schlank
and Nat Stapleton, we use this retract approach to do Hopkins-Kuhn-Ravenel character theory for all saturated fusion
systems by building on the theorems for finite p-groups.**

**Date: ****Wednesday, January 6, 2016**

**Time: ****14.00-15.00**

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

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

**Sune**** Precht Reeh will be visiting our
department for a week between January 2-10. **