Tait colorings, and an instanton homology for webs and foams

  • Peter B. Kronheimer

    Harvard University, Cambridge, USA
  • Tomasz S. Mrowka

    Massachusetts Institute of Technology, Cambridge, USA
Tait colorings, and an instanton homology for webs and foams cover
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Abstract

We use 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 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.

Cite this article

Peter B. Kronheimer, Tomasz S. Mrowka, Tait colorings, and an instanton homology for webs and foams. J. Eur. Math. Soc. 21 (2019), no. 1, pp. 55–119

DOI 10.4171/JEMS/831