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Book Synopsis
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.

Trees of Hyperbolic Spaces

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    Order before 4pm today for delivery by Mon 22 Jun 2026.

    By Michael Kapovich

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      View other formats and editions of Trees of Hyperbolic Spaces by Michael Kapovich

      Publisher: American Mathematical Society
      Publication Date: 1/7/2024
      ISBN13: 9781470474256, 978-1470474256
      ISBN10: 1470474255

      Description

      Book Synopsis
      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.

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