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

Gruber, Dominik; Sisto, Alessandro; Tessera, Romain

doi:10.1090/proc/14754

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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