Measure conjugacy invariants for actions of countable sofic groups
| dc.creator | Bowen, Lewis | |
| dc.date | 2008-04-22 | |
| dc.date | 2009-04-15 | |
| dc.date.accessioned | 2026-07-07T13:03:33Z | |
| dc.date.available | 2026-07-07T13:03:33Z | |
| dc.description | Sofic groups were defined implicitly by Gromov in [Gr99] and explicitly by Weiss in [We00]. All residually finite groups (and hence every linear group) is sofic. The purpose of this paper is to introduce, for every countable sofic group $G$, a family of measure-conjugacy invariants for measure-preserving $G$-actions on probability spaces. These invariants generalize Kolmogorov-Sinai entropy for actions of amenable groups. They are computed exactly for Bernoulli shifts over $G$, leading to a complete classification of Bernoulli systems up to measure-conjugacy for many groups including all countable linear groups. Recent rigidity results of Y. Kida and S. Popa are utilized to classify Bernoulli shifts over mapping class groups and property T groups up to orbit equivalence and von Neumann equivalence respectively. | |
| dc.description | v.6 corrects a few minor errors | |
| dc.identifier | https://arxiv.org/abs/0804.3582 | |
| dc.identifier | http://arxiv.org/abs/0804.3582 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226839 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A35 | |
| dc.title | Measure conjugacy invariants for actions of countable sofic groups | |
| dc.type | text |