Beyond Hyperbolicity

Mark Hagen (University of Bristol), Richard Webb (University of Cambridge), Henry Wilton (University of Cambridge)

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English

Cambridge University Press
11 July 2019

Groups & group theory; Non-Euclidean geometry; Topology

Series: London Mathematical Society Lecture Note Series

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.

Edited by: Mark Hagen (University of Bristol), Richard Webb (University of Cambridge), Henry Wilton (University of Cambridge)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 228mm, Width: 152mm, Spine: 15mm
Weight: 380g
ISBN: 9781108447294
ISBN 10: 1108447295
Series: London Mathematical Society Lecture Note Series
Pages: 440
Publication Date: 11 July 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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 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 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.

Reviews for Beyond Hyperbolicity

'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