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

Analysis and Geometry in Metric Spaces (2016)

- Volume: 4, Issue: 1, page 160-186, electronic only
- ISSN: 2299-3274

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topTim Austin. "The Geometry of Model Spaces for Probability-Preserving Actions of Sofic Groups." Analysis and Geometry in Metric Spaces 4.1 (2016): 160-186, electronic only. <http://eudml.org/doc/286763>.

@article{TimAustin2016,

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.},

author = {Tim Austin},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {Sofic entropy; Bernoulli system; Popa factor; model spaces; connectedness; sofic entropy},

language = {eng},

number = {1},

pages = {160-186, electronic only},

title = {The Geometry of Model Spaces for Probability-Preserving Actions of Sofic Groups},

url = {http://eudml.org/doc/286763},

volume = {4},

year = {2016},

}

TY - JOUR

AU - Tim Austin

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

JO - Analysis and Geometry in Metric Spaces

PY - 2016

VL - 4

IS - 1

SP - 160

EP - 186, electronic only

AB - 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.

LA - eng

KW - Sofic entropy; Bernoulli system; Popa factor; model spaces; connectedness; sofic entropy

UR - http://eudml.org/doc/286763

ER -

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