Stable Andrews-Curtis Conjecture via Fake Surfaces and Zeeman Conjecture

TL;DR

This paper introduces an induction scheme to prove the stable Andrews-Curtis conjecture, showing that all low-complexity contractible fake surfaces are 3-deformable to a point, advancing understanding of surface deformability.

Contribution

It presents a novel induction approach linking fake surfaces to the stable Andrews-Curtis conjecture and proves the conjecture for surfaces of complexity less than 6.

Findings

All contractible fake surfaces of complexity less than 6 are 3-deformable to a point.

The proposed induction scheme connects fake surfaces with the stable Andrews-Curtis conjecture.

The approach provides a new method to verify surface deformability in topological conjectures.

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.