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Geodesics in Trees of Hyperbolic and Relatively Hyperbolic Spaces

Part of: Special aspects of infinite or finite groups Low-dimensional topology

Published online by Cambridge University Press:  20 November 2015

François Gautero
François Gautero*
Affiliation:
Université de Nice Sophia Antipolis, Parc Valrose, Laboratoire de Mathématiques J. A. Dieudonné, UMR CNRS 7351, 06108 Nice Cedex 02, France ([email protected])
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Abstract

We present a careful approximation of the quasi-geodesics of trees of hyperbolic and relatively hyperbolic spaces. As an application we prove a dynamical and geometric combination theorem for trees of relatively hyperbolic spaces, with both Farb's and Gromov's definitions.

Keywords

Gromov hyperbolicityFarb and Gromov relative hyperbolicitytrees of spacesmapping toricombination theorem

MSC classification

Secondary: 20F65: Geometric group theory 57M50: Geometric structures on low-dimensional manifolds
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 3 , August 2016 , pp. 701 - 740
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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