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2019 Uniform exponential growth for CAT(0) square complexes
Aditi Kar, Michah Sageev
Algebr. Geom. Topol. 19(3): 1229-1245 (2019). DOI: 10.2140/agt.2019.19.1229

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 1 0 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, 2 1 0 , 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.

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Aditi Kar. Michah Sageev. "Uniform exponential growth for CAT(0) square complexes." Algebr. Geom. Topol. 19 (3) 1229 - 1245, 2019. https://doi.org/10.2140/agt.2019.19.1229

Information

Received: 21 August 2017; Revised: 18 June 2018; Accepted: 5 November 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07142601
MathSciNet: MR3954280
Digital Object Identifier: 10.2140/agt.2019.19.1229

Subjects:
Primary: 20F65

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 3 • 2019
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