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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.
Keywords: $\mathrm{CAT}(0)$ cube complex, divergence, Coxeter group, right-angled Coxeter group
Levcovitz, Ivan 1
@article{10_2140_agt_2018_18_1633,
author = {Levcovitz, Ivan},
title = {Divergence of {CAT(0)} cube complexes and {Coxeter} groups},
journal = {Algebraic and Geometric Topology},
pages = {1633--1673},
publisher = {mathdoc},
volume = {18},
number = {3},
year = {2018},
doi = {10.2140/agt.2018.18.1633},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.1633/}
}
TY - JOUR AU - Levcovitz, Ivan TI - Divergence of CAT(0) cube complexes and Coxeter groups JO - Algebraic and Geometric Topology PY - 2018 SP - 1633 EP - 1673 VL - 18 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.1633/ DO - 10.2140/agt.2018.18.1633 ID - 10_2140_agt_2018_18_1633 ER -
Levcovitz, Ivan. Divergence of CAT(0) cube complexes and Coxeter groups. Algebraic and Geometric Topology, Tome 18 (2018) no. 3, pp. 1633-1673. doi: 10.2140/agt.2018.18.1633
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