Rigidity for Quasi-Mobius group actions
classification
🧮 math.MG
math.GR
keywords
groupboundaryhyperbolicspaceactionsahlforsdimensionfinite
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Suppose G is a hyperbolic group whose boundary has topological dimension k. If the boundary is quasisymmetrically homeomorphic to an Ahlfors k-regular metric space, then, modulo a finite normal subgroup, G is isomorphic to a uniform lattice in the isometry group of hyperbolic (k+1)-space.
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