Trees of Hyperbolic Spaces

Michael Kapovich, Pranab Sardar (Autoren)

Buch | Softcover

278 Seiten

2024
American Mathematical Society (Verlag)
978-1-4704-7425-6 (ISBN)

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Offering an alternative proof of the Bestvina-Feighn theorem for trees of hyperbolic spaces, the work defines uniform quasigeodesics and demonstrates Cannon-Thurston maps for subtrees and relatively hyperbolic spaces. It probes laminations and discusses key group-theoretic outcomes.

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

Erscheinungsdatum	22.08.2024
Reihe/Serie	Mathematical Surveys and Monographs
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-7425-5 / 1470474255
ISBN-13	978-1-4704-7425-6 / 9781470474256
Zustand	Neuware