Journal article
Solid Ergodicity and Orbit Equivalence Rigidity for Coinduced Actions
International mathematics research notices, Vol.2022(11), pp.8251-8279
05/17/2022
DOI: 10.1093/imrn/rnaa325
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.
Details
- Title: Subtitle
- Solid Ergodicity and Orbit Equivalence Rigidity for Coinduced Actions
- Creators
- Daniel Drimbe - University of Regina
- Resource Type
- Journal article
- Publication Details
- International mathematics research notices, Vol.2022(11), pp.8251-8279
- DOI
- 10.1093/imrn/rnaa325
- ISSN
- 1073-7928
- eISSN
- 1687-0247
- Publisher
- Oxford Univ Press
- Number of pages
- 29
- Grant note
- Pacific Institute for the Mathematical Sciences fellowship
- Language
- English
- Date published
- 05/17/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984696655602771
Metrics
3 Record Views