Groups acting amenably on their Higson corona

Alexander Engel

Vol. 341 (2026), No. 1, 45–67

DOI: 10.2140/pjm.2026.341.45

Abstract

We investigate groups that act amenably on their Higson corona (also known as bi-exact groups) and provide reformulations of this in relation to the stable Higson corona, nuclearity of crossed products and to positive type kernels.

We further investigate implications of this in relation to the Baum–Connes conjecture, and prove that Gromov hyperbolic groups have isomorphic equivariant $K$-theories of their Gromov boundary and their stable Higson corona.

Keywords

amenable actions, Higson corona, Baum–Connes conjecture, bi-exact groups

Mathematical Subject Classification

Primary: 19K35

Secondary: 46L80, 47L65, 51F30

Milestones

Received: 31 August 2024

Revised: 11 November 2025

Accepted: 21 November 2025

Published: 10 March 2026