2015/08/28 by P. B. Kronheimer, Kronheimer, P. B., Tomasz Mrowka +1 · 3 citations
Mathematics · #05C15 (secondary) #57R58 (primary) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1508.07205
openalex publication_date 2015/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.