The Geometry of Model Spaces for Probability-Preserving Actions of Sofic Groups

• Autorzy: Tim Austin
• Języki publikacji: EN

Abstrakty

EN

Bowen’s notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the ‘model spaces’. The metric geometry of these model spaces can exhibit various interesting features, some of which provide other invariants of the action. This paper explores an approximate connectedness property of the model spaces, and uses it give a new proof that certain groups admit factors of Bernoulli shifts which are not Bernoulli. This was originally proved by Popa. Our proof covers fewer examples than his, but provides additional information about this phenomenon.

Słowa kluczowe

EN

Sofic entropy; Bernoulli system; Popa factor; model spaces; connectedness

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2016-02-19

zaakceptowano

2016-06-06

online

2016-08-29

Twórcy

autor

Tim Austin

• Courant Institute, New York University, 251 Mercer St, New York, NY 10012, U.S.A.

Identyfikatory

DOI

10.1515/agms-2016-0006