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

Dominik Gruber; Alessandro Sisto; Romain Tessera

doi:10.1090/proc/14754

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

Dominik Gruber
, Alessandro Sisto
, Romain Tessera

ETH Zurich
Laboratoire de Mathématiques d'Orsay

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2773-2782
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	7
DOIs	https://doi.org/10.1090/proc/14754
Publication status	Published - 1 Jul 2020
Externally published	Yes

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title = "Random Gromov's monsters do not act non-elementarily on hyperbolic spaces",

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.",

author = "Dominik Gruber and Alessandro Sisto and Romain Tessera",

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AB - 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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JO - Proceedings of the American Mathematical Society

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

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