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arXiv · 1508.07205

Tait colorings, and an instanton homology for webs and foams

P. B. Kronheimer·T. S. Mrowka
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Abstract

We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. We prove a non-vanishing theorem for this SO(3) instanton homology of webs, using Gabai's sutured manifold theory. It is hoped that the non-vanishing theorem may support a program to provide a new proof of the four-color theorem.

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P. B. Kronheimer, T. S. Mrowka. 2015-08-28. Tait colorings, and an instanton homology for webs and foams. https://arxiv.org/abs/1508.07205

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