Tait colorings, and an instanton homology for webs and foams

By P. Kronheimer, T. Mrowka. Journal of the European Mathematical Society (Print), 2015

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

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