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3 - Acylindrically hyperbolic groups

from Part One - LECTURES

Published online by Cambridge University Press:  22 June 2019

Edited by
Mark Hagen ,
Richard Webb  and
Henry Wilton
Mark Hagen
Affiliation:
University of Bristol
Richard Webb
Affiliation:
University of Cambridge
Henry Wilton
Affiliation:
University of Cambridge
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Summary

These are notes from a mini-course lectured by Denis Osin on acylindrically hyperbolic groups given at Beyond Hyperbolicity in Cambridge in June 2016. In this course we will be looking at acylindrically hyperbolic groups. Such groups make up a large portion of the "universe of finitely presented groups" described in Martin Bridson's course. Through examples of such groups we shall see that this class is indeed a large portion of the universe, but we shall also see that there is much we can prove. In particular, we will discuss results on small-cancellation theory and Dehn fillings, as well as some newer results.

Keywords

hyperbolic groupacylindrically hyperbolic groupacylindrical actionweak proper discontinuitysmall-cancellationSQ-universal grouphyperbolically embedded subgroupDehn surgeryacylindrically hyperbolic structure
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Chapter
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Beyond Hyperbolicity , pp. 65 - 80
Publisher: Cambridge University Press
Print publication year: 2019

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