On uniform Hilbert Schmidt stability of groups
Abstract
A group $\Gamma$ is said to be uniformly HS stable if any map $\varphi : \Gamma \to U(n)$ that is almost a unitary representation (w.r.t. the Hilbert Schmidt norm) is close to a genuine unitary representation of the same dimension. We present a complete classification of uniformly HS stable groups among finitely generated residually finite ones. Necessity of the residual finiteness assumption is discussed. A similar result is shown to hold assuming only amenability.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.10304
 Bibcode:
 2020arXiv201010304A
 Keywords:

 Mathematics  Group Theory
 EPrint:
 10 pages. Revised introduction and references. To appear in Proceedings of the American Mathematical Society