Stable Andrews-Curtis Conjecture via Fake Surfaces and Zeeman Conjecture
Geometric Topology
2026-01-09 v2 Group Theory
Abstract
We propose an induction scheme that aims at establishing the stable Andrews-Curtis conjecture in the affirmative. The stable Andrews-Curtis conjecture is equivalent to the conjecture that every contractible fake surface is 3-deformable to a point. We prove that every contractible fake surface of complexity less than 6 is 3-deformable to a point by induction.
Keywords
Cite
@article{arxiv.2412.12293,
title = {Stable Andrews-Curtis Conjecture via Fake Surfaces and Zeeman Conjecture},
author = {Lucas Fagan and Yang Qiu and Zhenghan Wang},
journal= {arXiv preprint arXiv:2412.12293},
year = {2026}
}
Comments
17 pages, 22 figures