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
Groups acting on CAT(0) cube complexes with uniform exponential growth

Radhika Gupta, Kasia Jankiewicz and Thomas Ng

Algebraic & Geometric Topology 23 (2023) 13–42
Abstract

We study uniform exponential growth of groups acting on CAT(0) cube complexes. We show that groups acting without global fixed points on CAT(0) square complexes either have uniform exponential growth or stabilize a Euclidean subcomplex. This generalizes the work of Kar and Sageev that considers free actions. Our result lets us show uniform exponential growth for certain groups that act improperly on CAT(0) square complexes, namely, finitely generated subgroups of the Higman group and triangle-free Artin groups. We also obtain that nonvirtually abelian groups acting freely on CAT(0) cube complexes of any dimension with isolated flats that admit a geometric group action have uniform exponential growth.

Keywords
uniform exponential growth, CAT(0) cube complexes
Mathematical Subject Classification
Primary: 20E07, 20F65, 20F67
Secondary: 57M60
References
Publication
Received: 8 July 2020
Revised: 19 September 2021
Accepted: 24 October 2021
Published: 27 March 2023
Authors
Radhika Gupta
School of Mathematics
Tata Institute of Fundamental Research
Mumbai
India
Kasia Jankiewicz
Department of Mathematics
University of California, Santa Cruz
Santa Cruz, CA
United States
Thomas Ng
Mathematics Department
Technion - Israel Institute of Technology
Haifa
Israel

Open Access made possible by participating institutions via Subscribe to Open.