Hyperfiniteness and Borel asymptotic dimension of boundary actions of hyperbolic groups

Abstract

We give a new short proof of the theorem due to Marquis and Sabok, which states that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group on its Gromov boundary is hyperfinite. Our methods permit moreover to show that every such action has finite Borel asymptotic dimension.

10 pages, comments welcome