Representation spaces and MOY's quantum invariants of graphs

Motivated by Kronheimer and Mrowka's discovery of the relationship between Khovanov homology of knots and singular SU(2) instanton Floer homology of knots and links, we were lead to explore possible generalizations to higher rank bundles. It then appears natural to consider representation spaces of planar bi-coloured trivalent graphs, rather than just knots, and we get a surprising relationship between these representation spaces and quantum invariants of planar graphs. This is joint work with Andrew Lobb.