Logo image
Solid Ergodicity and Orbit Equivalence Rigidity for Coinduced Actions
Journal article   Peer reviewed

Solid Ergodicity and Orbit Equivalence Rigidity for Coinduced Actions

Daniel Drimbe
International mathematics research notices, Vol.2022(11), pp.8251-8279
05/17/2022
DOI: 10.1093/imrn/rnaa325
url
https://arxiv.org/pdf/2003.03708View
Open Access

Abstract

We prove that the solid ergodicity property is stable with respect to taking coinduction for a fairly large class of coinduced action. More precisely, assume that Sigma < Gamma are countable groups such that g Sigma g(-1) boolean AND Sigma is finite for any g is an element of Gamma \ Sigma . Then any measure preserving action Sigma boolean AND X-0 gives rise to a solidly ergodic equivalence relation if and only if the equivalence relation of the associated coinduced action Gamma boolean AND X is solidly ergodic. We also obtain orbit equivalence rigidity for such actions by showing that the orbit equivalence relation of a rigid or compact measure preserving action Sigma boolean AND X-0 of a property (T) group is "remembered" by the orbit equivalence relation of Gamma boolean AND X.
Mathematics Physical Sciences Science & Technology

Details

Metrics

Logo image