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- Mark Hagen, University of Bristol
- Richard Webb, University of Cambridge
- Henry Wilton, University of Cambridge
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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.Read more
- 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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- Date Published: July 2019
- format: Adobe eBook Reader
- isbn: 9781108598491
- contains: 24 b/w illus.
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
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