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arXiv · 2608.17036

Hyperbolic models and stability recognition for Coxeter groups

Christopher H. Cashen·Michelle Chu·Jing Tao
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Abstract

Given a finite rank Coxeter system, we construct a hyperbolic space by coning off the wide parabolic subcomplexes of its Davis complex. The resulting space is `stability recognizing', in the sense that stable subspaces of the Davis complex are exactly the quasigeodesically connected subspaces whose images in the coned-off space are quasiisometrically embedded. Equivalently, the coned-off space is `Morse recognizing': a quasigeodesic in the Davis complex is Morse if and only if it is quasigeodesic in the coned-off space. Furthermore, the action of the Coxeter group on this space gives its largest acylindrically hyperbolic structure.

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Christopher H. Cashen, Michelle Chu, Jing Tao. 2026-08-17. Hyperbolic models and stability recognition for Coxeter groups. https://arxiv.org/abs/2608.17036

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