Equivalence relations that act on bundles of hyperbolic spaces
Dynamical Systems
2016-12-13 v3 Operator Algebras
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 {\em 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), study the existence and residuality of different types of elements and obtain an analogue of Tits' alternative.
Keywords
Cite
@article{arxiv.1506.02727,
title = {Equivalence relations that act on bundles of hyperbolic spaces},
author = {Lewis Bowen},
journal= {arXiv preprint arXiv:1506.02727},
year = {2016}
}
Comments
this version is the final version