Equivalence relations that act on bundles of hyperbolic spaces

Consider a measured equivalence relation acting on a bundle of hyperbolic metric spaces by isometries. We prove that every aperiodic hyperfinite subequivalence relation is contained in a unique maximal hyperfinite subequivalence relation. We classify elements of the full group according to their act...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2018-10, Vol.38 (7), p.2447-2492
Main Author: BOWEN, LEWIS
Format: Article
Language:English
Subjects:
Equivalence
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Summary:Consider a measured equivalence relation acting on a bundle of hyperbolic metric spaces by isometries. We prove that every aperiodic hyperfinite subequivalence relation is contained in a unique maximal hyperfinite subequivalence relation. We classify elements of the full group according to their action on fields on boundary measures (extending earlier results of Kaimanovich [Boundary amenability of hyperbolic spaces. Discrete Geometric Analysis (Contemporary Mathematics, 347). American Mathematical Society, Providence, RI, 2004, pp. 83–111]), study the existence and residuality of different types of elements and obtain an analog of Tits’ alternative.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2016.145