Rigidity of amalgamated free products in measure equivalence
نویسندگان
چکیده
منابع مشابه
Free Entropy Dimension in Amalgamated Free Products
We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some ‘exotic’ Popa algebra generators of free group factors are shown to have the expected free entropy dimension. We also show that microstates and non–microstates free entropy dimension agree f...
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We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.
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We study rigidity properties of lattices in Isom(H) SOn,1(R), n ≥ 3, and of surface groups in Isom(H2) SL2(R) in the context of integrable measure equivalence. The results for lattices in Isom(H), n ≥ 3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. Despite the lack of Mostow rigidity for n = 2 we ...
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ژورنال
عنوان ژورنال: Journal of Topology
سال: 2011
ISSN: 1753-8416
DOI: 10.1112/jtopol/jtr012