Hyperbolic models and stability recognition for Coxeter groups

Christopher H. Cashen, Michelle Chu, Jing Tao

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.

Disclosure

“□ ϵ ϵ AI use The authors used several versions of the AI tool ChatGPT as interactive sounding boards to explore possible proof strategies and test their arguments. The conception of the arguments and the writing of this paper were done by the authors.”
PDF page 56

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T05:20:18.598352Z

Structural counts

Pages 58 pdf

Theorems 17 source

Lemmas 54 source

Propositions 22 source

Corollaries 19 source

Definitions 30 source

Displayed equations 165 source

Bibliography entries 77 source

Appendix pages 2 estimated

Count notes

Source counts use the expanded primary TeX file main.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.