Nilpotent slices, Hilbert schemes, and the Jones polynomial
Symplectic Geometry
2007-05-23 v3 Geometric Topology
Abstract
Seidel and Smith have constructed an invariant of links as the Floer cohomology for two Lagrangians inside a complex affine variety Y. This variety is the intersection of a semisimple orbit with a transverse slice at a nilpotent in the Lie algebra We exhibit bijections between a set of generators for the Seidel-Smith cochain complex, the generators in Bigelow's picture of the Jones polynomial, and the generators of the Heegaard Floer cochain complex for the double branched cover. This is done by presenting Y as an open subset of the Hilbert scheme of a Milnor fiber.
Keywords
Cite
@article{arxiv.math/0411015,
title = {Nilpotent slices, Hilbert schemes, and the Jones polynomial},
author = {Ciprian Manolescu},
journal= {arXiv preprint arXiv:math/0411015},
year = {2007}
}
Comments
43 pages, 13 figures; revised version, to appear in Duke Math. J