Geodesic
Uniform exponential growth for CAT(0) square complexes
Kar, Aditi1 ; Sageev, Michah2
1 Department of Mathematics, Royal Holloway, University of London, Egham, United Kingdom
2 Department of Mathematics, Israel Institute of Technology, Haifa, Israel
Algebraic and Geometric Topology, Tome 19 (2019) no. 3, pp. 1229-1245

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2019.19.1229
Classification : 20F65
Keywords: uniform exponential growth, CAT(0) cubical groups

Kar, Aditi 1 ; Sageev, Michah 2

1 Department of Mathematics, Royal Holloway, University of London, Egham, United Kingdom
2 Department of Mathematics, Israel Institute of Technology, Haifa, Israel 
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Kar, Aditi; Sageev, Michah. Uniform exponential growth for CAT(0) square complexes. Algebraic and Geometric Topology, Tome 19 (2019) no. 3, pp. 1229-1245. doi: 10.2140/agt.2019.19.1229

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