SO(3) Homology of Graphs and Links
Benjamin Cooper, Matt Hogancamp, Vyacheslav Krushkal
TL;DR
This paper extends Khovanov homology to categorify the SO(3) Kauffman polynomial and planar graph chromatic polynomial, providing new structural insights and computations for knots and spin networks.
Contribution
It introduces a novel categorification framework for the SO(3) Kauffman polynomial and planar graph chromatic polynomial, expanding the scope of Khovanov homology.
Findings
Homologies of knots and spin networks computed
Structural properties of the categorifications analyzed
New computational techniques developed
Abstract
The SO(3) Kauffman polynomial and the chromatic polynomial of planar graphs are categorified by a unique extension of the Khovanov homology framework. Many structural observations and computations of homologies of knots and spin networks are included.
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