Measure equivalence and right-angled Artin groups
Appears in collection : Measured and Geometric Group Theory, Rigidity, Operator Algebras / Théorie mesurée et géométrique des groupes, rigidité, algèbres d’opérateurs
Given a finite simple graph X, the right-angled Artin group associated to X is defined by the following very simple presentation: it has one generator per vertex of X, and the only relations consist in imposing that two generators corresponding to adjacent vertices commute. We investigate right-angled Artin groups from the point of view of measured group theory. Our main theorem is that two right-angled Artin groups with finite outer automorphism groups are measure equivalent if and only if they are isomorphic. On the other hand, right-angled Artin groups are never superrigid from this point of view: given any right-angled Artin group G, I will also describe two ways of producing groups that are measure equivalent to G but not commensurable to G.This is joint work with Jingyin Huang.
