A link invariant from the symplectic geometry of nilpotent slices
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).
Keywords
Cite
@article{arxiv.math/0405089,
title = {A link invariant from the symplectic geometry of nilpotent slices},
author = {Paul Seidel and Ivan Smith},
journal= {arXiv preprint arXiv:math/0405089},
year = {2007}
}
Comments
v2: minor change to the introduction (grading in the long exact sequence corrected). v3: referees' suggestions and corrections incorporated; major changes to section 2 (the general Lie theory simplified by narrowing scope to sl_n) and minor changes to section 4 (more background on Floer theory included). This version to appear in Duke Mathematical Journal