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

Tim 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 -