Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 19, Number 3 (2019), 1229-1245.
Uniform exponential growth for CAT(0) square complexes
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 is a finite collection of hyperbolic automorphisms of a CAT(0) square complex , then either there exists a pair of words of length at most in which freely generate a free semigroup, or all elements of stabilize a flat (of dimension or in ). As a corollary, we obtain a lower bound for the growth constant, , 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.
Algebr. Geom. Topol., Volume 19, Number 3 (2019), 1229-1245.
Received: 21 August 2017
Revised: 18 June 2018
Accepted: 5 November 2018
First available in Project Euclid: 29 May 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Kar, Aditi; Sageev, Michah. Uniform exponential growth for CAT(0) square complexes. Algebr. Geom. Topol. 19 (2019), no. 3, 1229--1245. doi:10.2140/agt.2019.19.1229. https://projecteuclid.org/euclid.agt/1559095424