Gromov's random monsters do not act non-elementarily on hyperbolic spaces
classification
🧮 math.GR
keywords
hyperbolicspacesgraphsgromovgroupsnon-elementarilyrandomacting
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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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