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Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.
List of contents
Preface; 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.
About the author
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.
Summary
This book focuses on generalisations of Gromov hyperbolicity in geometric group theory. Five self-contained expository articles introduce topics 'beyond hyperbolicity': these can be used as an introduction for students or as a reference for experts. The final part contains research articles on the latest results in this rich and active field.
