# Automorphisms and splittings of special groups

19.10.2021 15:00 - 17:00

Elia Fioravanti (MPIM-Bonn)

The automorphism group of a discrete group $$G$$ can often be described quite explicitly in terms of the amalgamated-product and HNN splittings of $$G$$ over a family of subgroups. In the introductory talk, I will discuss the classical case when $$G$$ is a Gromov-hyperbolic group (originally due to Rips and Sela), highlighting some of the techniques involved. The research talk will then focus on automorphisms of "special groups", a broad family of subgroups of right-angled Artin groups introduced by Haglund and Wise. The main result is that, when $$G$$ is special, the outer automorphism group $$\mathrm{Out}(G)$$ is infinite if and only if $$G$$ splits over a centraliser or closely related subgroups. A similar result holds for automorphisms that preserve a coarse median structure on $$G$$.

Based on arXiv:2108.13212.

Join Zoom meeting ID 978 1075 8446 or via the link below. Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)

Organiser:

Location:
Zoom