"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
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.