Ric Wade

Translation properness for untwisted automorphism groups of RAAGs

A finitely generated group G is said to be translation proper if the asymptotic translation length of any infinite order element is uniformly bounded below on some (equivalently, any) Cayley graph of G. Translation properness implies that cyclic subgroups of G are undistorted, and a result of Conner states that furthermore solvable subgroups of finite virtual cohomological dimension in G are virtually abelian. We aim to show that the untwisted automorphism group of a right-angled Artin group is translation proper. Combining this with work of Charney-Vogtmann and Horbez shows that these groups satisfy a strengthened Tits alternative. This is work-in-progress with Jerónimo García-Mejía.