Department of
Applied
Mathematics

Knot Homologies and Graph Polynomials

Iain Moffatt

Abstract

By considering Khovanov's categorification of the Jones polynomial, we construct a bi-graded homology theory for embedded graphs whose Euler characteristic is equal to the chromatic polynomial and whose homology groups are strictly stronger invariants. We will show that the homology is independent of the planar embedding of a graph and that this is not the case for embeddings on higher genus surfaces. The relationship with knot theory and Khovanov homology will be emphasised throughout.