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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access August 29, 2016

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

  • Tim Austin


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.


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Received: 2016-2-19
Accepted: 2016-6-6
Published Online: 2016-8-29

© 2016 Tim Austin

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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