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A link invariant from the symplectic geometry of nilpotent slices

Paul Seidel·Ivan Smith
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Abstract

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).

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Paul Seidel, Ivan Smith. 2006-04-18. A link invariant from the symplectic geometry of nilpotent slices. https://arxiv.org/abs/math/0405089

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