The dimension of Kronheimer-Mrowka instanton homology group for plane trivalent graphs

2022/02/26 by Zipei Zhuang, Zhuang, Zipei
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2202.13091

openalex publication_date 2022/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We proved that the dimension of the F-vector space J#(G) for a plane trivalent graph G, defined by Kronheimer and Mrowka using their SO(3) instanton Floer homology, is equal to the number of Tait colorings of G.

Related

• SU(3) instanton homology for webs and foams
• Tait coloring and a moduli space
• Tait colorings, and an instanton homology for webs and foams
• Foam evaluation and Kronheimer--Mrowka theories
• Instantons and Khovanov homology in \mathbbRP³