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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.
Gupta, Radhika 1 ; Jankiewicz, Kasia 2 ; Ng, Thomas 3
@article{10_2140_agt_2023_23_13,
author = {Gupta, Radhika and Jankiewicz, Kasia and Ng, Thomas},
title = {Groups acting on {CAT(0)} cube complexes with uniform exponential growth},
journal = {Algebraic and Geometric Topology},
pages = {13--42},
publisher = {mathdoc},
volume = {23},
number = {1},
year = {2023},
doi = {10.2140/agt.2023.23.13},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.13/}
}
TY - JOUR AU - Gupta, Radhika AU - Jankiewicz, Kasia AU - Ng, Thomas TI - Groups acting on CAT(0) cube complexes with uniform exponential growth JO - Algebraic and Geometric Topology PY - 2023 SP - 13 EP - 42 VL - 23 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.13/ DO - 10.2140/agt.2023.23.13 ID - 10_2140_agt_2023_23_13 ER -
%0 Journal Article %A Gupta, Radhika %A Jankiewicz, Kasia %A Ng, Thomas %T Groups acting on CAT(0) cube complexes with uniform exponential growth %J Algebraic and Geometric Topology %D 2023 %P 13-42 %V 23 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.13/ %R 10.2140/agt.2023.23.13 %F 10_2140_agt_2023_23_13
Gupta, Radhika; Jankiewicz, Kasia; Ng, Thomas. Groups acting on CAT(0) cube complexes with uniform exponential growth. Algebraic and Geometric Topology, Tome 23 (2023) no. 1, pp. 13-42. doi: 10.2140/agt.2023.23.13
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