2004/05/05 by Seidel, Paul, Smith, Ivan · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.math/0405089
Using the symplectic geometry of certain manifolds which appear naturally in Lie theory, we define an invariant which assigns a graded abelian group to an oriented link. The relevant manifolds are transverse slices to certain nilpotent orbits inside sl2m, and intersections of those with regular semisimple orbits. The invariant is conjectured to be equal to Khovanov's combinatorially defined homology theory (with the bigrading of that theory collapsed in a certain way).