Hyperbolic groups with boundary an n-dimensional Sierpinski space

Bena Tshishiku; Jean-Fran\c{c}ois Lafont

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Hyperbolic groups with boundary an n-dimensional Sierpinski space

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arxiv 1505.03817 v1 pith:O6DVCK4K submitted 2015-05-14 math.GT math.GR

Hyperbolic groups with boundary an n-dimensional Sierpinski space

Jean-Fran\c{c}ois Lafont , Bena Tshishiku This is my paper

classification math.GT math.GR

keywords boundaryhyperbolicsierpinskispaceasphericaldimensionalgroupvisual

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For n>6, we show that if G is a torsion-free hyperbolic group whose visual boundary is an (n-2)-dimensional Sierpinski space, then G=\pi_1(W) for some aspherical n-manifold W with nonempty boundary. Concerning the converse, we construct, for each n>3, examples of aspherical manifolds with boundary, whose fundamental group G is hyperbolic, but with visual boundary not homeomorphic to an (n-2)-dimensional Sierpinski space.

Hyperbolic groups with boundary an n-dimensional Sierpinski space

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