Volume 11, issue 4 (2011)

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$\mathrm{SO}(3)$ homology of graphs and links

Benjamin Cooper, Matt Hogancamp and Vyacheslav Krushkal

Algebraic & Geometric Topology 11 (2011) 2137–2166
Abstract

The $SO\left(3\right)$ 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.

Keywords
categorification, Khovanov homology, Kauffmann polynomial, chromatic polynomial, spin network
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25, 05C10, 05C31