ORBIT INEQUIVALENT ACTIONS OF NON-AMENABLE GROUPS

By Inessa Epstein. 2007

55 citations recorded by the source corpus.

Considertwo freemeasurepreservinggroupactions y (X,µ),� y (X,µ), and a measure preserving actiony a (Z,�) where (X,µ),(Z,�) are standard probability spaces. We show how to construct free measure preserv- ing actions y c (Y,m), � y d (Y,m) on a standard probability space such that E dE c and d has a as a factor. This generalizes the standard notion of co-induction of actions of groups from actions of subgroups. We then use this construction to show that if is a countable non-amenable group, then admits continuum many orbit inequivalent free, measure preserving, ergodic actions on a standard probability space.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/290b2fa199772de277419834ed9b9e12731d3bd2

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Citations in the corpus

A SURVEY OF MEASURED GROUP THEORY (2009, methodology): “The ultimate solution to the problem, covering all nonamenable groups, was shortly obtained by Inessa Epstein [36] using a result by Damien Gaboriau and Russel Lyons [60], who proved that any nonamenable contains an F2 in a sort of measure-theoretical sense.”
Global Aspects of Ergodic Group Actions (2010, methodology): “If [E] was weakly dense in Aut(X,μ), A would be T -invariant for any T ∈ Aut(X,μ), which is absurd.”
Orbit inequivalent actions for groups containing a copy of $\mathbb{F}_{2}$ (2006, methodology): “Since von Neumann equivalence of actions is weaker than orbit equivalence ([FM]) this result generalizes Theorem 1.3. as well as the main result of [ E ].”