Follow-up Workshop to TP Rigidity

Date: April 27 - May 1, 2015
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: Wolfgang Lück, Romain Tessera

This meeting was a follow-up workshop to the Hausdorff Trimester Program "Rigidity".

Speakers: Arthur Bartels, Mladen Bestvina, Martin Bridson, Nigel Higson, Wolfgang Lück, Denis Osin, Mark Sapir, Romain Tessera, Christian Wegner, Guoliang Yu

Schedule
Partipants

Main objectives of the meeting:

Methods from geometric group theory have recently played a crucial role in the proof of the Farrell-Jones conjecture for a large class of groups including hyperbolic groups. This proof essentially splits into a K-theoretic part and a purely group geometric part. This workshop will be entirely dedicated to the second (geometric) part, so that no background in K-theory or L-theory is requested.

The geometric part of the Farrell-Jones conjecture heavily relies on a notion of geodesic flow on hyperbolic spaces and CAT(0)-spaces. The geodesic flow is used in a very non-trivial way to obtain certain equivariant covering properties for hyperbolic groups which are then used as an input for the proof of the Farrell-Jones conjecture.

Our aim is two-fold:

1) These equivariant coverings are intriguing and extremely non-trivial, even for the free group. One goal of this meeting would be to understand the proof of their existence, and idealy to obtain a simpler and more explicit construction for the free group.

2) Recent developments successfully extended hyperbolic methods to a large class of non-hyperbolic groups including Mapping Class Groups and Out(F_n). Generalizing these equivariant coverings to this setting could possibly yield a proof of the Farrell-Jones conjecture for theses groups. Perhaps more importantly, we believe that this would highlight new geometric features about these groups.