Exactness of groups and amenability at infinity

Specialeforsvar: Frederik Brandt

Titel: Exactness of groups and amenability at infinity

Abstract: This thesis examines the interplay between the notions of KW-exactness and amenability at infinity for second countable locally compact groups. In particular, we explore a recent paper by Brodzki, Cave and Li (partially) settling in the positive a long-time conjecture by Anantharaman-Delaroche on the equivalence of the two notions. To this end, we draw upon
various results from the pioneering work of Kirchberg and Wassermann on exactness, and Anantharaman-Delaroche on C∗-dynamical systems and amenability of actions. Also, we present some basics on coarse geometry and investigate the so-called "Property A" defined by Yu and Roe for proper metric spaces of bounded geometry. We establish a tightly-woven connection between Property A and amenability at infinity and, ultimately, manageto reproduce the work of Brodzki, Cave and Li.

Vejleder: Mikael Rørdam
Censor:    James Gabe, SDU