Boundaries of Hyperbolic Metric Spaces

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We investigate the relationship between the metric boundary and the Gromov boundary of a hyperbolic metric space. We show that the Gromov boundary is a quotient topological space of the metric boundary, and that therefore a word-hyperbolic group has an amenable action on the metric boundary of its Cayley graph. This result has significance for the study of Lip-norms on group C*-algebras.
9 pages. AMSLaTeX

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Metric Geometry, Group Theory, Operator Algebras, 20F65 (Primary) 46L87, 53C23 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/68773

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0310101
 http://arxiv.org/abs/math/0310101

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arXiv