Random Gromov’s monsters do not act non-elementarily on hyperbolic spaces | Zendy

Dominik Gruber | Zendy; Alessandro Sisto | Zendy; Romain Tessera | Zendy

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

Author(s) -

Dominik Gruber,

Alessandro Sisto,

Romain Tessera

Publication year - 2020

Publication title -

proceedings of the american mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.968

H-Index - 84

eISSN - 1088-6826

pISSN - 0002-9939

DOI - 10.1090/proc/14754

Subject(s) - monster , mathematics , geodesic , hyperbolic group , relatively hyperbolic group , random walk , pure mathematics , combinatorics , discrete mathematics , hyperbolic manifold , mathematical analysis , hyperbolic function , statistics , physics , quantum mechanics

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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