  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 sl_{2m}, 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).
