Automorphisms and splittings of special groups

Abstract: 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 \(G\).

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar