Higher A-Homotopy Vanishing for Coxeter Chamber Graphs
Manuscript 11 October 2026 · Online 11 October 2026
Abstract
We prove that the standard Cayley graph of every finite-rank Coxeter system has trivial \(A\)-homotopy groups in all degrees \(j\geq2\). The argument replaces the Coxeter group by the right-angled Coxeter group retaining exactly its commuting relations. Short closed walks lift, and every finite image in the resulting median graph admits a based contraction through graph maps.
A direct lattice-lifting proof checks the exterior basepoint condition and explains why degree one is different. For a finite real reflection group, the theorem establishes the all-degree group comparison for the real 3-parabolic arrangement by combining higher-\(A\) vanishing with the previously known fundamental-group comparison and classical asphericity of the complement.
The right-angled construction, degree-one kernel and classical median-graph results are credited to earlier work. The result concerns \(k=3\), not the general comparison for \(k>3\). This preprint is AI-assisted, self-audited and unrefereed, with no independent review, formal verification or absolute priority claim.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Coxeter higher-A vanishing theorem
- Categories
- math.AT · math.CO · math.GR
- Manuscript
- 11 October 2026
- Online release
- 11 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Higher A-Homotopy Vanishing for Coxeter Chamber Graphs,” EulerSolve Research Papers, AIM-TOPOLOGY-0097, 2026. https://doi.org/10.5281/zenodo.23291327.
BibTeX
@misc{ferudun2026coxeterhighera,
author = {Ferudun, Alper},
title = {Higher A-Homotopy Vanishing for Coxeter Chamber Graphs},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/aim-topology-0097/},
doi = {10.5281/zenodo.23291327},
note = {AIM-TOPOLOGY-0097; unrefereed preprint}
}