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Groups acting on CAT(0)
cube complexes with uniform exponential growth
Radhika Gupta, Kasia Jankiewicz and Thomas Ng |
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Algebraic & Geometric Topology 23 (2023) 13–42
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Abstract |
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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
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Mathematical Subject Classification
Primary: 20E07, 20F65, 20F67
Secondary: 57M60
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References |
Publication
Received: 8 July 2020
Revised: 19 September 2021
Accepted: 24 October 2021
Published: 27 March 2023
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Authors |
| Radhika Gupta | |
| School of Mathematics Tata Institute of Fundamental Research Mumbai India |
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| Kasia Jankiewicz | |
| Department of Mathematics University of California, Santa Cruz Santa Cruz, CA United States |
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| Thomas Ng | |
| Mathematics Department Technion - Israel Institute of Technology Haifa Israel |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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