The Farrell­–Tate K-theory of Out(Fn)Geometric Group Theory Oberseminar

by Dr Naomi Andrew (Université Paris-Saclay)

Wednesday Dec 10, 2025, 11:00 AM → 12:00 PM Europe/Berlin

Endenicher Allee 60/0-008 (Mathezentrum)

Given a (nice enough) group, there is an isomorphism, due to Lück, relating the rationalised K-theory groups of its classifying space to a large product of cohomology groups, some with rational and some with p-adic coeffecients.

In recent joint work with Irakli Patchkoria, we identify a generalised cohomology theory capturing the p-adic part of this product. Working in Out(Fn), in ranks close to p we can fully compute this p-adic part and in this way produce an infinite family of odd-dimensional summands in the rationalised K-theory of Out(Fn).