Bonn Topology Group - Abstracts

General Information - Members - Activities - Topology Seminar

Talk

October 31, 2023
Sam Hughes (University of Oxford): Centralisers and classifying spaces for Out(F_N)

Abstract

In this talk I will outline reduction theory for mapping classes and explain various attempts to construct similar machinery for elements of Out(F_N). I will then present a new reduction theory for studying centralisers of elements in IA_3(N), the finite index level 3 congruence subgroup of Out(F_N). Using this I will explain an application to the classifying space for virtually cyclic subgroups, a space notable for its appearance in the Farrell--Jones Conjecture. Based on joint work with Yassine Guerch and Luis Jorge Sánchez Saldaña.