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.
General
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