Measure equivalence rigidity among the Higman groups (Camille Horbez, Paris-Saclay)

20.09.2022 10:30

The Higman groups were introduced in 1951 (by Higman) as the first examples of infinite finitely presented groups with no nontrivial finite quotient. They have a simple presentation, with k\ge 4 generators, where two consecutive generators (considered cyclically) generate a Baumslag-Solitar subgroup. Higman groups have received a lot of attention and remain mysterious in many ways. We prove a rigidity theorem for many Higman groups from the viewpoint of measured group theory, and measure equivalence (a notion introduced by Gromov as a measure-theoretic analogue of quasi-isometry). More precisely, let H be a Higman group on at least 5 generators, and let G be any countable group. If G and H are measure equivalent, then they are virtually isomorphic. I will explain the motivation and context behind this theorem, some consequences, and describe some of the tools arising in its proof. This is joint work with Jingyin Huang.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire "Groupes et géométrie"

entrée libre