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• W2981890251 abstract "Two groups have a common model geometry if they act properly and cocompactly by isometries on the same proper geodesic metric space. We consider free products of uniform lattices in isometry groups of rank-1 symmetric spaces and prove, within each quasi-isometry class, that residually finite groups that have a common model geometry are abstractly commensurable. Our result gives the first examples of hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. An important component of the proof is a generalization of Leighton’s graph covering theorem. The main theorem depends on residual finiteness, and we show that finite extensions of uniform lattices in rank-1 symmetric spaces that are not residually finite would give counterexamples." @default.
• W2981890251 created "2019-11-01" @default.
• W2981890251 creator A5053780435 @default.
• W2981890251 creator A5086230233 @default.
• W2981890251 date "2023-07-03" @default.
• W2981890251 modified "2023-10-18" @default.
• W2981890251 title "Action rigidity for free products of hyperbolic manifold groups" @default.
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• W2981890251 doi "https://doi.org/10.5802/aif.3585" @default.
• W2981890251 hasPublicationYear "2023" @default.
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