The dimension of Kronheimer-Mrowka instanton homology group for plane trivalent graphs
Zipei Zhuang
TL;DR
This paper proves that the dimension of the Kronheimer-Mrowka instanton homology group for a plane trivalent graph equals the number of Tait colorings, linking topological invariants with graph coloring.
Contribution
It establishes a direct equality between the dimension of the instanton homology group and Tait colorings for plane trivalent graphs, a novel connection in topological graph theory.
Findings
Dimension of J#(G) equals the number of Tait colorings
Links instanton Floer homology to classical graph coloring
Provides new insights into topological invariants of graphs
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology