Nilpotent slices, Hilbert schemes, and the Jones polynomial
Nilpotent slices, Hilbert schemes, and the Jones polynomial
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幂零切片、希尔伯特方案和琼斯多项式
DOI：
10.1215/s0012-7094-06-13224-6
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发表时间：
2004
影响因子：
2.5
通讯作者：
Ciprian Manolescu
中科院分区：
文献类型：
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作者：
Ciprian Manolescu
Seidel和Smith构造了复仿射簇Y中两个拉格朗日量的一个链环不变量作为Floer上同调。这个簇是李代数$sl_{2 m}中一个半单轨道在幂零点处与一个横切片的交。我们展示了一组发电机之间的双射的Seidel-Smith cochain复杂的，发电机在毕格罗的图片的琼斯多项式，和发电机的Heegaard Floer cochain复杂的双分支覆盖。这是通过将Y呈现为Milnor纤维的Hilbert方案的开子集来完成的。
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 $sl_{2m}.$ 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.