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Trees of Hyperbolic Spaces
 
Michael Kapovich University of California, Davis, CA
Pranab Sardar Indian Institute of Science Education and Research, Mohali, India
Softcover ISBN:  978-1-4704-7425-6
Product Code:  SURV/282
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-7778-3
Product Code:  SURV/282.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7425-6
eBook: ISBN:  978-1-4704-7778-3
Product Code:  SURV/282.B
List Price: $260.00 $197.50
MAA Member Price: $234.00 $177.75
AMS Member Price: $208.00 $158.00
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Trees of Hyperbolic Spaces
Michael Kapovich University of California, Davis, CA
Pranab Sardar Indian Institute of Science Education and Research, Mohali, India
Softcover ISBN:  978-1-4704-7425-6
Product Code:  SURV/282
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-7778-3
Product Code:  SURV/282.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7425-6
eBook ISBN:  978-1-4704-7778-3
Product Code:  SURV/282.B
List Price: $260.00 $197.50
MAA Member Price: $234.00 $177.75
AMS Member Price: $208.00 $158.00
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2822024; 278 pp
    MSC: Primary 20; 51

    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.

    Readership

    Graduate students and researchers interested in hyperbolic geometry.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2822024; 278 pp
MSC: Primary 20; 51

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.

Readership

Graduate students and researchers interested in hyperbolic geometry.

  • Chapters
  • 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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