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arXiv · 1910.14437

Geometry of right-angled Coxeter groups on the Croke-Kleiner spaces

Yulan Qing
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Abstract

In this paper we study the right-angled Coxeter groups that acts geometrically on the Salvetti complex of a certain right-angled Artin group, which we refer to as Croke-Kleiner spaces. We prove that any right-angled Coxeter group that acts geometrically on the Croke-Kleiner spaces acts with $\pi/2$ angles between reflecting axes, while the quasi-isometric right-angled Artin group can act with angles that are any real number in the range $(0, \pi/2]$. The contrast between the two examples shows that in this case a right-angled Coxeter group is geometrically more "rigid" than its quasi isometric counterpart.

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Yulan Qing. 2019-10-29. Geometry of right-angled Coxeter groups on the Croke-Kleiner spaces. https://doi.org/10.1007/s10711-016-0149-1

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