Volume 19, issue 3 (2019)

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

Volume 23
Issue 9, 3909–4400
Issue 8, 3417–3908
Issue 7, 2925–3415
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

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
Subscriptions
 
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.
Uniform exponential growth for CAT(0) square complexes

Aditi Kar and Michah Sageev

Algebraic & Geometric Topology 19 (2019) 1229–1245
Abstract

We start the inquiry into proving uniform exponential growth in the context of groups acting on CAT(0) cube complexes. We address free group actions on CAT(0) square complexes and prove a more general statement. This says that if F is a finite collection of hyperbolic automorphisms of a CAT(0) square complex X, then either there exists a pair of words of length at most 10 in F which freely generate a free semigroup, or all elements of F stabilize a flat (of dimension 1 or 2 in X). As a corollary, we obtain a lower bound for the growth constant, 210, which is uniform not just for a given group acting freely on a given CAT(0) cube complex, but for all groups which are not virtually abelian and have a free action on a CAT(0) square complex.

PDF Access Denied

We have not been able to recognize your IP address 18.206.48.243 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:

Keywords
uniform exponential growth, CAT(0) cubical groups
Mathematical Subject Classification 2010
Primary: 20F65
References
Publication
Received: 21 August 2017
Revised: 18 June 2018
Accepted: 5 November 2018
Published: 21 May 2019
Authors
Aditi Kar
Department of Mathematics
Royal Holloway, University of London
Egham
United Kingdom
Michah Sageev
Department of Mathematics
Israel Institute of Technology
Haifa
Israel