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Proceedings of the American Mathematical Society

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Random Gromov's monsters do not act non-elementarily on hyperbolic spaces


Authors: Dominik Gruber, Alessandro Sisto and Romain Tessera
Journal: Proc. Amer. Math. Soc. 148 (2020), 2773-2782
MSC (2010): Primary 20F65
DOI: https://doi.org/10.1090/proc/14754
Published electronically: March 18, 2020
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Abstract: We show that Gromov's monster groups arising from i.i.d. labelings of expander graphs do not admit non-elementary actions on geodesic hyperbolic spaces. The proof relies on comparing properties of random walks on randomly labeled graphs and on groups acting non-elementarily on hyperbolic spaces.


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Additional Information

Dominik Gruber
Affiliation: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
Email: dominik.gruber@math.ethz.ch

Alessandro Sisto
Affiliation: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
Email: sisto@math.ethz.ch

Romain Tessera
Affiliation: Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France
Email: tessera@phare.normalesup.org

DOI: https://doi.org/10.1090/proc/14754
Received by editor(s): June 6, 2017
Received by editor(s) in revised form: March 13, 2019, and May 17, 2019
Published electronically: March 18, 2020
Communicated by: Kenneth Bromberg
Article copyright: © Copyright 2020 Dominik Gruber, Alessandro Sisto, and Romain Tessera