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

Tim Austin

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)160-186
Number of pages27
JournalAnalysis and Geometry in Metric Spaces
Volume4
Issue number1
DOIs
StatePublished - 2016

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Applied Mathematics

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