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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Random Gromov’s monsters do not act non-elementarily on hyperbolic spaces
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by Dominik Gruber, Alessandro Sisto and Romain Tessera PDF
Proc. Amer. Math. Soc. 148 (2020), 2773-2782

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
  • MR Author ID: 1089843
  • Email: dominik.gruber@math.ethz.ch
  • Alessandro Sisto
  • Affiliation: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
  • MR Author ID: 881750
  • Email: sisto@math.ethz.ch
  • Romain Tessera
  • Affiliation: Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France
  • MR Author ID: 800491
  • Email: tessera@phare.normalesup.org
  • 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
  • © Copyright 2020 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
  • MathSciNet review: 4099767