The Borel Conjecture for hyperbolic and CAT(0)-groups

TL;DR

This paper proves the Borel Conjecture for a broad class of groups, including hyperbolic and certain CAT(0) groups, advancing understanding in geometric topology and group actions.

Contribution

It establishes the Borel Conjecture for groups acting properly, isometrically, and cocompactly on finite-dimensional CAT(0) spaces, extending previous results to new group classes.

Findings

Proves the Borel Conjecture for hyperbolic groups.

Extends the conjecture to groups acting on CAT(0) spaces.

Provides new techniques for topological rigidity in geometric group theory.

Abstract

We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)-space.