TY - CHAP
T1 - Uniformly recurrent subgroups
AU - Glasner, Eli
AU - Weiss, Benjamin
N1 - Publisher Copyright:
© 2015 American Mathematical Society.
PY - 2015
Y1 - 2015
N2 - We define the notion of uniformly recurrent subgroup, URS in short, which is a topological analog of the notion of invariant random subgroup (IRS), introduced in Abert, Glasner, and Virag (2014). Our main results are as follows. (i) It was shown in Weiss (2012) that for an arbitrary countable infinite group G, any free ergodic probability measure preserving G-system admits a minimal model. In contrast we show here, using URS’s, that for the lamplighter group there is an ergodic measure preserving action which does not admit a minimal model. (ii) For an arbitrary countable group G, every URS can be realized as the stability system of some topologically transitive G-system.
AB - We define the notion of uniformly recurrent subgroup, URS in short, which is a topological analog of the notion of invariant random subgroup (IRS), introduced in Abert, Glasner, and Virag (2014). Our main results are as follows. (i) It was shown in Weiss (2012) that for an arbitrary countable infinite group G, any free ergodic probability measure preserving G-system admits a minimal model. In contrast we show here, using URS’s, that for the lamplighter group there is an ergodic measure preserving action which does not admit a minimal model. (ii) For an arbitrary countable group G, every URS can be realized as the stability system of some topologically transitive G-system.
KW - Essentially free action
KW - Free group
KW - IRS
KW - Invariant minimal subgroups
KW - Stability group
KW - Stability system
KW - URS
UR - http://www.scopus.com/inward/record.url?scp=85106793025&partnerID=8YFLogxK
U2 - 10.1090/conm/631/12596
DO - 10.1090/conm/631/12596
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AN - SCOPUS:85106793025
T3 - Contemporary Mathematics
SP - 63
EP - 75
BT - Contemporary Mathematics
PB - American Mathematical Society
ER -