C*-stability of discrete groups
Abstract
A group may be considered -stable if almost representations of the group in a -algebra are always close to actual representations. We initiate a systematic study of which discrete groups are -stable or only stable with respect to some subclass of -algebras, e.g. finite dimensional -algebras. We provide criteria and invariants for stability of groups and this allows us to completely determine stability/non-stability of crystallographic groups, finitely generated torsion-free step-2 nilpotent groups, surface groups, virtually free groups and certain Baumslag-Solitar groups.
Keywords
Cite
@article{arxiv.1808.06793,
title = {C*-stability of discrete groups},
author = {Søren Eilers and Tatiana Shulman and Adam P. W. Sørensen},
journal= {arXiv preprint arXiv:1808.06793},
year = {2021}
}
Comments
The results in section 4.2 (finitely generated torsion-free 2-step nilpotent groups) have been strengthened slightly. Clarified in the introduction that we only consider unitary group representations. A few misprints fixed. 39 pages