Abstract
We provide geometric conditions on a pair of hyperplanes of a 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 –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
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
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