Hyperbolic groups with 1-dimensional boundary

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dc.creatorKapovich, Michael
dc.creatorKleiner, Bruce
dc.date1998-06-11
dc.date.accessioned2026-07-07T05:25:00Z
dc.date.available2026-07-07T05:25:00Z
dc.descriptionIf a torsion-free hyperbolic group G has 1-dimensional boundary, then the boundary is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When the boundary of G is a Sierpinski carpet we show that G is a quasi-convex subgroup of a 3-dimensional hyperbolic Poincare duality group. We also construct a ``topologically rigid'' hyperbolic group G: any homeomorphism of the boundary of G is induced by an element of G.
dc.identifierhttps://arxiv.org/abs/math/9806059
dc.identifierhttp://arxiv.org/abs/math/9806059
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77030
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.titleHyperbolic groups with 1-dimensional boundary
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