Inner amenability for groups and central sequences in factors

TL;DR

This paper demonstrates that many groups with certain negative curvature properties are not inner amenable and that their associated group-measure space factors lack property Gamma, extending known results to new classes.

Contribution

It introduces a broad class of non-inner amenable groups satisfying negative curvature conditions and links these properties to the absence of property Gamma in related factors.

Findings

Many groups with negative curvature are not inner amenable

Group-measure space factors lack property Gamma for these groups

Results recover non-inner amenability of mapping class groups and Out(F_n)

Abstract

We show that a large class of i.c.c., countable, discrete groups satisfying a weak negative curvature condition are not inner amenable. By recent work of Hull and Osin, our result recovers that mapping class groups and Out(F_n) are not inner amenable. We also show that the group-measure space constructions associated to free, strongly ergodic p.m.p. actions of such groups do not have property Gamma of Murray and von Neumann.