Alexandre Martin

The Tits alternative for two-dimenional Artin groups

Many groups of geometric interest present an interesting dichotomy at the level of their subgroups: their subgroups are either very large (they contain a free subgroup) or very small (they are virtually abelian). In this talk, I will explain how one can use ideas from group actions in negative curvature to prove such a dichotomy. In particular, I will show how can prove such a strengthening of the Tits Alternative for a large class of Artin groups. This is joint work with Piotr Przytycki.