A Compact Cubulation of a Quadratic Free-by-Cyclic Group
Manuscript 18 October 2026 · Online 18 October 2026
Abstract
Let phi be the automorphism of F(a,b,c) given by phi(a)=a, phi(b)=ab and phi(c)=bcb. We construct a compact nonpositively curved cube complex with fundamental group F(a,b,c) semidirect_phi Z. It has one vertex, seven edges, eight squares and two three-dimensional cubes. Its universal cover gives a free, proper, cocompact action on a three-dimensional CAT(0) cube complex. The construction uses an explicit four-vertex cyclic core and a cubical involution; all link and presentation calculations are supplied. This answers the literal ab formulation in frozen UnsolvedMath record AIM-GEOMETRIC_GROUP_THEORY-0024. It does not address the distinct aba formulation in the workshop report. AI-assisted, self-audited and unrefereed; no absolute-priority or proof-assistant certification claim.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete proof (frozen ab formulation)
- Categories
- math.GR · math.GT
- Manuscript
- 18 October 2026
- Online release
- 18 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, “A Compact Cubulation of a Quadratic Free-by-Cyclic Group,” EulerSolve Research Papers, AIM-GEOMETRIC_GROUP_THEORY-0024, 2026. https://doi.org/10.5281/zenodo.23446961.
BibTeX
@misc{ferudun2026compactcubulation,
author = {Ferudun, Alper},
title = {A Compact Cubulation of a Quadratic Free-by-Cyclic Group},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/aim-geometric-group-theory-0024/},
doi = {10.5281/zenodo.23446961},
note = {AIM-GEOMETRIC_GROUP_THEORY-0024; unrefereed preprint}
}