
Trees of Hyperbolic Spaces
American Mathematical Society (Publisher)
Published on 31. August 2024
Book
Paperback/Softback
278 pages
978-1-4704-7425-6 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
ISBN-13
978-1-4704-7425-6 (9781470474256)
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Schweitzer Classification
Persons
Michael Kapovich, University of California, Davis, CA, and Pranab Sardar, Indian Institute of Science Education and Research, Mohali, India.
Content
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
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