Determination up to isomorphism of right-angled Coxeter systems

Abstract

In this paper, we announce that every right-angled Coxeter group determines its Coxeter system up to isomorphism. This implies that the Dranishnikov's rigidity conjecture is the case for right-angled Coxeter groups, i.e., every right-angled Coxeter group determines its boundary up to homeomorphism.