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Using the symplectic geometry of certain manifolds which appear naturally inLie theory, we define an invariant which assigns a graded abelian group to anoriented link. The relevant manifolds are transverse slices to certainnilpotent orbits inside sl_{2m}, and intersections of those with regularsemisimple orbits. The invariant is conjectured to be equal to Khovanov'scombinatorially defined homology theory (with the bigrading of that theorycollapsed in a certain way).

A link invariant from the symplectic geometry of nilpotent slices