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9781470474256 Academic Inspection Copy

Trees of Hyperbolic Spaces

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This book offers an alternative proof of the Bestvina-Feighn combination theorem for trees of hyperbolic spaces and describes uniform quasigeodesics in such spaces. As one of the applications of their description of uniform quasigeodesics, the authors prove the existence of Cannon-Thurston maps for inclusion maps of total spaces of subtrees of hyperbolic spaces and of relatively hyperbolic spaces. They also analyze the structure of Cannon-Thurston laminations in this setting. Furthermore, some group-theoretic applications of these results are discussed. This book also contains background material on coarse geometry and geometric group theory.
Michael Kapovich, University of California, Davis, CA, and Pranab Sardar, Indian Institute of Science Education and Research, Mohali, India.
Preliminaries on metric geometry Graphs of groups and trees of metric spaces Carpets, ladders, flow-spaces, metric bundles, and their retractions Hyperbolicity of ladders Hyperbolicity of flow-spaces Hyperbolicity of trees of spaces: Putting everything together Description of geodesics Cannon-Thurston maps Cannon-Thurston maps for elatively hyperbolic spaces
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