Sciweavers

BSL
2008

Hyperlinear and Sofic Groups: A Brief Guide

13 years 11 months ago
Hyperlinear and Sofic Groups: A Brief Guide
This is an introductory survey of the emerging theory of two new classes of (discrete, countable) groups, called hyperlinear and sofic groups. They can be characterized as subgroups of metric ultraproducts of families of, respectively, unitary groups U(n) and symmetric groups Sn, n N. Hyperlinear groups come from theory of operator algebras (Connes' Embedding Problem), while sofic groups, introduced by Gromov, are motivated by a problem of symbolic dynamics (Gottschalk's Surjunctivity Conjecture). Open questions are numerous, in particular it is still unknown if every group is hyperlinear and/or sofic.
Vladimir Pestov
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where BSL
Authors Vladimir Pestov
Comments (0)