## Duke Mathematical Journal

### Nilpotent slices, Hilbert schemes, and the Jones polynomial

Ciprian Manolescu

#### Abstract

Seidel and Smith [33] 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 $\mathfrak{sl}_{2m}.$ 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

#### Article information

Source
Duke Math. J. Volume 132, Number 2 (2006), 311-369.

Dates
First available in Project Euclid: 16 March 2006

https://projecteuclid.org/euclid.dmj/1142517220

Digital Object Identifier
doi:10.1215/S0012-7094-06-13224-6

Mathematical Reviews number (MathSciNet)
MR2219260

Zentralblatt MATH identifier
1110.57010

#### Citation

Manolescu, Ciprian. Nilpotent slices, Hilbert schemes, and the Jones polynomial. Duke Math. J. 132 (2006), no. 2, 311--369. doi:10.1215/S0012-7094-06-13224-6. https://projecteuclid.org/euclid.dmj/1142517220

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