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Equivalence relations that act on bundles of hyperbolic spaces

Published online by Cambridge University Press:  03 April 2017

LEWIS BOWEN
LEWIS BOWEN*
Affiliation:
Mathematics Department, 1 University Station C1200, University of Texas at Austin, TX 78712, USA email [email protected]
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Abstract

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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 7 , October 2018 , pp. 2447 - 2492
Copyright
© Cambridge University Press, 2017 

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