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Hyperfiniteness of boundary actions of hyperbolic groups

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Abstract

We prove that for every finitely generated hyperbolic group G, the action of G on its Gromov boundary induces a hyperfinite equivalence relation.

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Acknowledgements

We would like to thank the referee for many valuable comments.

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Authors and Affiliations

  1. UCLouvain, IRMP-MATH, Chemin du Cyclotron 2, 1348, Louvain-la-Neuve, Belgium

    Timothée Marquis

  2. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street W, Montreal, QC, H3A 0B9, Canada

    Marcin Sabok

  3. Instytut Matematyczny PAN, Sniadeckich 8, 00-656, Warsaw, Poland

    Marcin Sabok

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  1. Timothée Marquis
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Correspondence to Timothée Marquis.

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Communicated by Andreas Thom.

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T. Marquis was F.R.S.-FNRS Postdoctoral Researcher. M. Sabok: This research was partially supported by the NSERC through the Discovery Grant RGPIN-2015-03738, by the FRQNT (Fonds de recherche du Québec) grant Nouveaux chercheurs 2018-NC-205427 and by the NCN (National Science Centre, Poland) through the grants Harmonia no. 2015/18/M/ST1/00050 and 2018/30/M/ST1/00668.

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Marquis, T., Sabok, M. Hyperfiniteness of boundary actions of hyperbolic groups. Math. Ann. 377, 1129–1153 (2020). https://doi.org/10.1007/s00208-020-02001-9

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  • DOI: https://doi.org/10.1007/s00208-020-02001-9

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