A link invariant from the symplectic geometry of nilpotent slices

Details A link invariant from the symplectic geometry of nilpotent slices A link invariant from the symplectic geometry of nilpotent slices

2004-05-05

arxiv.org/abs/math/0405089v3

Mathematics

Symplectic Geometry

v2: minor change to the introduction (grading in the long exact sequence corrected). v3: referees' suggestions and corrections

Scientific paper

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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