Divergence of CAT(0) Cube Complexes and Coxeter Groups

Ivan Levcovitz

doi:10.2140/agt.2018.18.1633

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arXiv · 1611.04378

Divergence of CAT(0) Cube Complexes and Coxeter Groups

Ivan Levcovitz

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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-Thomas that addressed the class of 2-dimensional right-angled Coxeter groups. As another application, we provide an inductive graph theoretic criteria 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 which are not right-angled.

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BibTeX RIS

Ivan Levcovitz. 2016-11-14. Divergence of CAT(0) Cube Complexes and Coxeter Groups. https://doi.org/10.2140/agt.2018.18.1633

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