The mapping cone formula in Heegaard Floer homology and Dehn surgery on knots in S3
The mapping cone formula in Heegaard Floer homology and Dehn surgery on knots in S3
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Heegaard Floer 同调中的映射锥公式和 S3 结上的 Dehn 手术
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发表时间：
2014
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通讯作者：
Fyodor Gainullin
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作者：
Fyodor Gainullin
我们用从CFK^{infty}（K）$导出的同调数据，写出了在S^3 $中对纽结K$进行Dehn手术的结果的Heegaard Floer同调（作为任意域上的绝对分次向量空间）的$+$形式的显式公式。这使我们能够证明一些结果Dehn手术结在$S^3$。特别是，我们表明，对于一个固定的流形，只有100多个交替的结，可以通过手术产生它。这是对Lackenby和珀塞尔最近结果的改进。我们还推导出一个下界的纽结依赖于流形，他们给手术的属。还提出了一些新的限制塞弗特血管瘤手术。
We write down an explicit formula for the $+$ version of the Heegaard Floer homology (as an absolutely graded vector space over an arbitrary field) of the results of Dehn surgery on a knot $K$ in $S^3$ in terms of homological data derived from $CFK^{infty}(K)$. This allows us to prove some results about Dehn surgery on knots in $S^3$. In particular, we show that for a fixed manifold there are only finitely many alternating knots that can produce it by surgery. This is an improvement on a recent result by Lackenby and Purcell. We also derive a lower bound on the genus of knots depending on the manifold they give by surgery. Some new restrictions on Seifert fibred surgery are also presented.