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2018 Divergence of $\mathrm{CAT}(0)$ cube complexes and Coxeter groups
Ivan Levcovitz
Algebr. Geom. Topol. 18(3): 1633-1673 (2018). DOI: 10.2140/agt.2018.18.1633

Abstract

We provide geometric conditions on a pair of hyperplanes of a CAT ( 0 ) cube complex that imply divergence bounds for the cube complex. As an application, we classify all right-angled Coxeter groups with quadratic divergence and show right-angled Coxeter groups cannot exhibit a divergence function between quadratic and cubic. This generalizes a theorem of Dani and Thomas that addressed the class of 2 –dimensional right-angled Coxeter groups. As another application, we provide an inductive graph-theoretic criterion on a right-angled Coxeter group’s defining graph which allows us to recognize arbitrary integer degree polynomial divergence for many infinite classes of right-angled Coxeter groups. We also provide similar divergence results for some classes of Coxeter groups that are not right-angled.

Citation

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Ivan Levcovitz. "Divergence of $\mathrm{CAT}(0)$ cube complexes and Coxeter groups." Algebr. Geom. Topol. 18 (3) 1633 - 1673, 2018. https://doi.org/10.2140/agt.2018.18.1633

Information

Received: 6 March 2017; Revised: 8 January 2018; Accepted: 25 January 2018; Published: 2018
First available in Project Euclid: 26 April 2018

zbMATH: 06866409
MathSciNet: MR3784015
Digital Object Identifier: 10.2140/agt.2018.18.1633

Subjects:
Primary: 20F65
Secondary: 20F55, 57M99

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 3 • 2018
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