A deformation of instanton homology for webs

TL;DR

This paper introduces a deformation of instanton homology for webs using a local coefficient system, revealing that for planar webs, the deformed homology's rank matches the number of Tait colorings, linking topology and graph colorings.

Contribution

The authors construct a new deformation of instanton homology for webs and establish its rank correspondence with Tait colorings in planar cases.

Findings

Deformed instanton homology's rank equals Tait colorings for planar webs.

A local system of coefficients is used to deform the homology.

The deformation connects topological invariants with graph coloring.

Abstract

A deformation of the authors' instanton homology for webs is constructed by introducing a local system of coefficients. In the case that the web is planar, the rank of the deformed instanton homology is equal to the number of Tait colorings of the web.