Rigidity Theorems For Actions Of Product Groups And Countable Borel Equivalence Relations

By Greg Hjorth, Alexander S. Kechris. 2005

86 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f97787a141467488fa72e1d1b6b3a5a9ff1dbc41

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Citations in the corpus

Orbit Equivalence and Measured Group Theory (2010, background): “The converse does not hold in general [Sch81], [HK05].”
Cocycle and orbit equivalence superrigidity for malleable actions of w-rigid groups (2005, background): “Sec. 3 in [P4]), but may contain all non-amenable groups of the form = 0 × 1 with both i infinite, thus relating with the rigidity results of Monod-Shalom ([MoSh1,2]) and Hjorth-Kechr is ( [HjKe]).”
AMENABLE ACTIONS AND ALMOST INVARIANT SETS (2007, background): “In fact, the existence of almost invariant sets depends only on the orbit equivalence relation, which, in the ergodic case, is equivalent to non-E0-ergodicity (Jones–Schmidt [9]), while the existence of almost invariant vectors depends on the group action (see [7] again).”
A SURVEY OF MEASURED GROUP THEORY (2009, methodology): “The notion of the cost of an action/relation was introduced by Levitt [77] and developed by Damien Gaboriau [44, 45, 47]; the monographs [71] and [70] also contain an extensive discussion.”
Ideal bicombings for hyperbolic groups and applications (2003, background): “countable group Λ, then Γ and Λ are isomorphic. Moreover, with respect to some isomorphism Γ ∼= Λ the actions are isomorphic by a Borel isomorphism which induces the given orbit equivalence. See also [20] for related results in a somewhat diﬀerent setting. 1.5. The non-vanishing result of Theorem 3 ”
Borel Equivalence Relations (2010, background): “This subgroup will be amenable (see Appendix C [36]), which in turn provides a contradiction to the non-amenability of Γ × Z (see Appendix A [36] again).”
Orbit equivalence rigidity and bounded cohomology (2006, background): “ group; the latter statement was established for the particular case of inﬁnite center by S. Adams [A2]. Related results. In the framework of reducibility of Borel relations, G. Hjorth and A. Kechris [HK] established rigidity results for certain types of products in independent work carried out at a”
The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, unknown): “Hjorth-Kechris [44] showed a similar result.”
Global Aspects of Ergodic Group Actions (2010, methodology): “See Jones-Schmidt [JS] and Hjorth-Kechris [HK3], Appendix A, for some basic properties of this concept.”
Monotone complete C*‐algebras and generic dynamics (2012, methodology): “For, by applying deep results of Hjorth and Kechris [22], it is possible to exhibit a small, wild, hyperfinite factor which is not”
On the superrigidity of malleable actions with spectral gap (2006, background): “The results in Theorems 1.1 through 1.6 add to the plethora of rigidity phenomena involving product groups that have been discovered in recent years in group theory, OE ergodic theory, Borel equivalence relations and von Neumann algebras/II1 factors ([MoSh], [ HK ], [OP], [Mo], [BSh], etc).”