Author:
CHIFAN IONUT,SINCLAIR THOMAS,UDREA BOGDAN
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 [Groups with hyperbolically embedded subgroups. Algebr. Geom. Topol.13 (2013), 2635–2665], our result recovers that mapping class groups and $\text{Out}(\mathbb{F}_{n})$ 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 [On rings of operators IV. Ann. of Math. (2) 44 (1943), 716–808].
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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