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Beyond Hyperbolicity


Part of London Mathematical Society Lecture Note Series

Brian H. Bowditch, Martin R. Bridson, Benjamin Barrett, Matthew Cordes, Alessandro Sisto, Jason Behrstock, Indira Chatterji, Alexandre Martin, Daniel Groves, Henry Wilton, Francesca Iezzi, Kate M. Vokes
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  • Date Published: July 2019
  • availability: Available
  • format: Paperback
  • isbn: 9781108447294

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About the Authors
  • Since the notion was introduced by Gromov in the 1980s, hyperbolicity of groups and spaces has played a significant role in geometric group theory; hyperbolic groups have good geometric properties that allow us to prove strong results. However, many classes of interest in our exploration of the universe of finitely generated groups contain examples that are not hyperbolic. Thus we wish to go 'beyond hyperbolicity' to find good generalisations that nevertheless permit similarly strong results. This book is the ideal resource for researchers wishing to contribute to this rich and active field. The first two parts are devoted to mini-courses and expository articles on coarse median spaces, semihyperbolicity, acylindrical hyperbolicity, Morse boundaries, and hierarchical hyperbolicity. These serve as an introduction for students and a reference for experts. The topics of the surveys (and more) re-appear in the research articles that make up Part III, presenting the latest results beyond hyperbolicity.

    • Mini-courses and expository articles serve as an introduction and as a reference on generalisations of Gromov hyperbolicity
    • Short research articles on intriguing topics answer some interesting open questions
    • Suitable for graduate students and established researchers alike
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    Reviews & endorsements

    'The articles in this collection take the reader on a journey from foundational examples and definitions to state-of-the-art theorems and actively researched open problems … Students and those wanting to enter these fields of specialization will want to return to the surveys and expositions for inspiration as they engage with more specialized literature.' Robert Bell, MAA Reviews

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    Product details

    • Date Published: July 2019
    • format: Paperback
    • isbn: 9781108447294
    • length: 440 pages
    • dimensions: 228 x 152 x 15 mm
    • weight: 0.38kg
    • contains: 24 b/w illus.
    • availability: Available
  • Table of Contents

    Part I. Lectures:
    1. Notes on coarse median spaces Brian H. Bowditch
    2. Semihyperbolicity Martin R. Bridson
    3. Acylindrically hyperbolic groups Benjamin Barrett
    Part II. Expository Articles:
    4. A survey on Morse boundaries and stability Matthew Cordes
    5. What is a hierarchically hyperbolic space? Alessandro Sisto
    Part III. Research Articles:
    6. A counterexample to questions about boundaries, stability, and commensurability Jason Behrstock
    7. A note on the acylindrical hyperbolicity of groups acting on CAT(0) cube complexes Indira Chatterji and Alexandre Martin
    8. Immutability is not uniformly decidable in hyperbolic groups Daniel Groves and Henry Wilton
    9. Sphere systems, standard form, and cores of products of trees Francesca Iezzi
    10. Uniform quasiconvexity of the disc graphs in the curve graphs Kate M. Vokes.

  • Editors

    Mark Hagen, University of Bristol
    Mark Hagen is a Lecturer in Mathematics at the University of Bristol. His interests lie in geometric group theory, including in particular cubical/median geometry, mapping class groups, and their coarse-geometric generalisations.

    Richard Webb, University of Cambridge
    Richard Webb is an EPSRC Postdoctoral Fellow at the University of Cambridge and a Stokes Research Fellow at Pembroke College. He investigates the algebra and geometry of the mapping class group and its relatives, often using techniques and inspiration drawn from geometric group theory.

    Henry Wilton, University of Cambridge
    Henry Wilton is a Reader in Pure Mathematics at the University of Cambridge and a Fellow of Trinity College. He works in the fields of geometric group theory and low-dimensional topology. His interests include the subgroup structure of hyperbolic groups, questions of profinite rigidity, decision problems, and properties of 3-manifold groups.


    Brian H. Bowditch, Martin R. Bridson, Benjamin Barrett, Matthew Cordes, Alessandro Sisto, Jason Behrstock, Indira Chatterji, Alexandre Martin, Daniel Groves, Henry Wilton, Francesca Iezzi, Kate M. Vokes

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