Knot Floer homology of Whitehead doubles
Knot Floer homology of Whitehead doubles
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怀特海双打的结弗洛尔同源性
DOI：
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发表时间：
2006
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通讯作者：
M. Hedden
中科院分区：
文献类型：
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作者：
M. Hedden
本文研究了任意纽结K的有扭和无扭Whitehead对偶的纽结Floer同调不变量。根据K的不变量，给出了B HFK.D .K;t//的过滤链同伦类型的公式，其中D .K;t/表示t-扭曲的正（分别为。负数）-K的扣合的Whitehead double。特别是，该公式可以迭代使用，并可用于计算通过手术获得的流形上的怀特黑德双弗洛尔同调。一个直接的推论是。DC.K;t//D1，如果t 0不是平滑切片。另一个推论是通过将任意纽结K的补集粘到三叶形的补集上而得到的三流形的弗洛尔同调的封闭公式。
In this paper we study the knot Floer homology invariants of the twisted and untwisted Whitehead doubles of an arbitrary knot, K . A formula is presented for the filtered chain homotopy type of b HFK.D .K;t// in terms of the invariants for K , where D .K;t/ denotes the t ‐twisted positive (resp. negative)-clasped Whitehead double of K . In particular, the formula can be used iteratively and can be used to compute the Floer homology of manifolds obtained by surgery on Whitehead doubles. An immediate corollary is that . DC.K;t//D1 if t 0 are not smoothly slice. Another corollary is a closed formula for the Floer homology of the three-manifold obtained by gluing the complement of an arbitrary knot, K , to the complement of the trefoil.