Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T06:34:40.734Z Has data issue: false hasContentIssue false

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
Get access

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
Type
Chapter
Information
Beyond Hyperbolicity , pp. 65 - 80
Publisher: Cambridge University Press
Print publication year: 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×