Search

Only show content I have access to (0)

Chapters (1)

Articles (1)

Last month (1)

Last 3 months (1)

Last 6 months (1)

Last 12 months (1)

Last 3 years (1)

Over 3 years (1)

From year:

To year:

Apply

Mathematics (2)

curve graph

Proceedings of the Edinburgh Mathematical Society (1)

Cambridge University Press (1)

London Mathematical Society Lecture Note Series (1)

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
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 .

To save content items to your Kindle, first ensure no-reply@cambridge.org 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.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services Please confirm that you accept the terms of use.

×

Let S be an orientable, connected surface of finite topological type, with genus $g \leqslant 2$ , empty boundary and complexity at least 2; we prove that any graph endomorphism of the curve graph of S is actually an automorphism. Also, as a complement of the author’s previous results, we prove that under mild conditions on the complexity of the underlying surfaces, any graph morphism between curve graphs is induced by a homeomorphism of the surfaces.

To prove these results, we construct a finite subgraph whose union of iterated rigid expansions is the curve graph $\mathcal{C}(S)$ . The sets constructed, and the method of rigid expansion, are closely related to Aramayona and Leininger’s finite rigid sets. We prove as a consequence that Aramayona and Leininger’s rigid set also exhausts $\mathcal{C}(S)$ via rigid expansions. The combinatorial rigidity results follow as an immediate consequence, based on the author’s previous results.

10 - Uniform quasiconvexity of the disc graphs in the curve graphs
from Part Three - Research Articles
Edited by Mark Hagen, University of Bristol, Richard Webb, University of Cambridge, Henry Wilton, University of Cambridge
Book:

Beyond Hyperbolicity

Published online:

22 June 2019

Print publication:

11 July 2019, pp 223-231
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
Summary

We give a proof that there exists a universal constant K such that the disc graph associated to a surface S forming a boundary component of a compact, orientable 3-manifold M is K-quasiconvex in the curve graph of S. Our proof does not require the use of train tracks.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Graph morphisms and exhaustion of curve graphs of low-genus surfaces

10 - Uniform quasiconvexity of the disc graphs in the curve graphs

Summary

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Graph morphisms and exhaustion of curve graphs of low-genus surfaces

10 - Uniform quasiconvexity of the disc graphs in the curve graphs

Summary