On asymptotic stability of connective groups

Abstract

In their study of almost group representations, Manuilov and Mishchenko introduced and investigated the notion of asymptotic stability of a finitely presented discrete group. In this paper we establish connections between connectivity of amenable groups and asymptotic stability and exhibit new classes of asymptotically stable groups. In particular, we show that if $G$ is an amenable and connective discrete group whose classifying space $BG$ is homotopic to a finite simplicial complex, then $G$ is asymptotically stable.