Mathematics – Symplectic Geometry
Scientific paper
2004-05-05
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).
Seidel Paul
Smith Ivan
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