Stable Andrews-Curtis Conjecture via Fake Surfaces and Zeeman Conjecture

Lucas Fagan; Yang Qiu; Zhenghan Wang

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arXiv · 2412.12293

Stable Andrews-Curtis Conjecture via Fake Surfaces and Zeeman Conjecture

Lucas Fagan·Yang Qiu·Zhenghan Wang

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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.

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Lucas Fagan, Yang Qiu, Zhenghan Wang. 2024-12-16. Stable Andrews-Curtis Conjecture via Fake Surfaces and Zeeman Conjecture. https://arxiv.org/abs/2412.12293

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