Hyperbolic groups with low-dimensional boundary

Michael Kapovich, Bruce Kleiner

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)647-669
Number of pages23
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Issue number5
StatePublished - Sep 2000

ASJC Scopus subject areas

  • General Mathematics


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