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Hyperbolic groups with low-dimensional boundary
Published Web Location
https://doi.org/10.1016/s0012-9593(00)01049-1No data is associated with this publication.
Abstract
If a torsion-free hyperbolic group G has 1-dimensional boundary ∂∞G, then ∂∞G is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When ∂∞G is a Sierpinski carpet we show that G is a quasi-convex subgroup of a 3-dimensional hyperbolic Poincaré duality group. We also construct a "topologically rigid" hyperbolic group G: any homeomorphism of ∂∞G is induced by an element of G. © 2000 Éditions scientifiques et médicales Elsevier SAS.
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