Volume 21, issue 4 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
The compression body graph has infinite diameter

Joseph Maher and Saul Schleimer

Algebraic & Geometric Topology 21 (2021) 1817–1856

We show that the compression body graph, which is Gromov hyperbolic, has infinite diameter. Furthermore, every subgroup in the Johnson filtration of the mapping class group contains elements which act loxodromically on the compression body graph. Our methods give an alternative proof of a result of Biringer, Johnson and Minsky: the stable lamination of a pseudo-Anosov element is contained in the limit set of a compression body if and only if some power of the pseudo-Anosov element extends over a nontrivial subcompression body. We also extend results of Lubotzky, Maher and Wu, on the distribution of Casson invariants of random Heegaard splittings, to a larger class of random walks.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

curve complex, disc set, handlebody, compression body
Mathematical Subject Classification 2010
Primary: 37E30
Secondary: 20F65, 57M50
Received: 7 October 2019
Revised: 3 July 2020
Accepted: 19 July 2020
Published: 18 August 2021
Joseph Maher
Department of Mathematics
CUNY College of Staten Island and CUNY Graduate Center
Staten Island, NY
United States
Saul Schleimer
Mathematics Institute
University of Warwick
United Kingdom