Nicholas Touikan

On the quasi-isometry and commensurability classification of low height constructible groups

I will first present my joint result with Alex Taam. Let G be the fundamental group of a space obtained by attaching closed surfaces together by tubes along systems of filling curves, then any group H quasi-isometric to G has a finite index subgroup H' isomorphic to a finite index subgroup G'of G. I will then discuss how this result fits within a larger project of understanding commensurability within the class of constructible hyperbolic groups.