The geometry of Higman groups
Event details
| Date | 19.11.2015 |
| Hour | 13:00 › 14:00 |
| Speaker | Alexandre Martin (Vienna) |
| Location | |
| Category | Conferences - Seminars |
The Higman group was constructed as the first example of a finitely
presented infinite group without non-trivial finite quotients. Despite
this pathological behaviour, I will describe striking similarities with
mapping class groups of hyperbolic surfaces, outer automorphisms of free
groups and special linear groups over the integers. The main object of
study will be the cocompact action of the group on a CAT(0) square complex
naturally associated to its standard presentation. This action, which
turns out to be intrinsic, can be used to explicitly compute the
automorphism group of the Higman group, and to show that the group is both
Hopfian and co-Hopfian, among other things.
If time allows, I will also mention the action of generalised Higman
groups on associated CAT(-1) polygonal complexes, and show that their
dynamical properties push the analogy with mapping class groups even
further.
presented infinite group without non-trivial finite quotients. Despite
this pathological behaviour, I will describe striking similarities with
mapping class groups of hyperbolic surfaces, outer automorphisms of free
groups and special linear groups over the integers. The main object of
study will be the cocompact action of the group on a CAT(0) square complex
naturally associated to its standard presentation. This action, which
turns out to be intrinsic, can be used to explicitly compute the
automorphism group of the Higman group, and to show that the group is both
Hopfian and co-Hopfian, among other things.
If time allows, I will also mention the action of generalised Higman
groups on associated CAT(-1) polygonal complexes, and show that their
dynamical properties push the analogy with mapping class groups even
further.
Links
Practical information
- General public
- Free