Uniform exponential growth for CAT(0) square complexes

Aditi Kar, Michah Sageev

Research output: Contribution to journalArticlepeer-review

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,10√2, 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.

Original languageEnglish
Pages (from-to)1229-1245
Number of pages17
JournalAlgebraic and Geometric Topology
Volume19
Issue number3
DOIs
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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