Component Symmetry and Tightness in Dimension Two
Manuscript 19 October 2026 · Online 19 October 2026
Abstract
For a finite nonempty simplicial complex of dimension at most two, we prove that tightness over a field of characteristic two is equivalent to a complete one-skeleton together with symmetry of the link-component counts in every induced subcomplex. The proof adapts the cycle-link argument of Bagchi, Datta and Spreer and fills induced link cycles using mod-two fundamental chains of the resulting closed surfaces. Consequently, tightness over any field implies tightness over F2 in dimension two. A four-vertex disk refutes the literal component-symmetry conjecture in the 2015 Oberwolfach report when neighbourliness is omitted; the theorem proves its neighbourly repair. This is an AI-assisted, self-audited, unrefereed preprint, not a claim of higher-dimensional field independence or certified absolute priority.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Counterexample and repaired theorem
- Categories
- math.AT · math.CO
- Manuscript
- 19 October 2026
- Online release
- 19 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, “Component Symmetry and Tightness in Dimension Two,” EulerSolve Research Papers, OWR-13490-013, 2026. https://doi.org/10.5281/zenodo.23477149.
BibTeX
@misc{ferudun2026componentsymmetry,
author = {Ferudun, Alper},
title = {Component Symmetry and Tightness in Dimension Two},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/owr-13490-013/},
doi = {10.5281/zenodo.23477149},
note = {OWR-13490-013; unrefereed preprint}
}