Groups and Operator Algebras Seminar

Speaker: Andrea Vaccaro (WWU Münster)

Title: Hyperfiniteness and Borel asymptotic dimension of boundary actions of hyperbolic groups

Abstract: In 1984 Weiss' asked whether the orbit equivalence relation of a Borel action of an amenable group on a standard Borel space is automatically hyperfinite. In this talk we investigate the analogous question in the setting of amenable actions of hyperbolic groups. In particular, we give a new short proof of Marquis and Sabok' result that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group on its Gromov boundary is hyperfinite. We expand moreover their result and show that any such action has finite Borel asymptotic dimension.

GOA website: https://sites.google.com/view/copenhagen-goa-seminar