Bi-exactness of Negatively Curved Groups

Abstract

Bi-exactness is an analytic property of groups introduced by Ozawa. This property provided a fundamentally new way to prove primeness of group von Neumann algebras and has been intensively studied from operator algebraic perspective. On the other hand, bi-exactness is not well understood from group theoretic perspective. Indeed, not many examples of bi-exact groups are found. Also, bi exactness is not preserved under some basic group theoretic constructions. The purpose of this dissertation is to study bi-exactness from group theoretic perspective by discovering a new permanence property of bi-exactness and a new class of bi-exact groups.