Inner amenability for groups and central sequences in factors

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.

first version. comments welcome!

References in corpus (2)

• Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)
• Structure of $\mathrm{I}{\mathrm{I}}_1$ factors arising from free Bogoljubov actions of arbitrary groups

Cited by in corpus (4)

• On acylindrical hyperbolicity of groups with positive first ${\ell }^2$-Betti number
• Invariant means and the structure of inner amenable groups
• Tensor product decompositions of II${}_1$ factors arising from extensions of amalgamated free product groups
• Stable actions of central extensions and relative property (T)