Homotopy Types and Shelling Certificates for the H3 Absolute Order
Manuscript 20 October 2026 · Online 20 October 2026
Abstract
We compute the homotopy type of the absolute order of the finite Coxeter group \(H_3\) after deleting its identity. The resulting complex is homotopy equivalent to a wedge of four circles and 872 two-spheres. Deleting the central involution as well gives a shellable wedge of 867 two-spheres. The ideals generated by classical and dual Coxeter elements are different: after deleting the identity, they are shellable wedges of 163 and 367 two-spheres, respectively. These assertions have explicit finite shelling certificates covering 4080 facets, checked by a standalone exact program that reconstructs the group and order. The link of the central involution is the disjoint union of five hexagons. It obstructs Cohen-Macaulayness and shellability for the full \(H_3\) complex, and the same interval gives an obstruction in \(H_4\). This addresses exceptional cases, not the uniform AIM classification. AI-assisted, self-audited and unrefereed; no independent review, formal verification or absolute priority claim.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete H3 calculation
- Categories
- math.CO · math.AT · math.GR
- Manuscript
- 20 October 2026
- Online release
- 20 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, “Homotopy Types and Shelling Certificates for the H3 Absolute Order,” EulerSolve Research Papers, AIM-PROBABILITY-0153, 2026. https://doi.org/10.5281/zenodo.23503571.
BibTeX
@misc{ferudun2026h3absolute,
author = {Ferudun, Alper},
title = {Homotopy Types and Shelling Certificates for the H3 Absolute Order},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/aim-probability-0153/},
doi = {10.5281/zenodo.23503571},
note = {AIM-PROBABILITY-0153; unrefereed preprint}
}