On Heegaard Floer homology and Seifert fibered surgeries
On Heegaard Floer homology and Seifert fibered surgeries
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论 Heegaard Floer 同源性和 Seifert 纤维手术
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Z. Szabó
中科院分区：
文献类型：
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作者：
P. Ozsváth;Z. Szabó
我们探讨了三球体中结的某些限制，这些限制允许进行非平凡的 Seifert 纤维手术。这些限制源于 Seifert 纤维空间的 Heegaard Floer 同源性，因此它们对此类结的亚历山大多项式及其结 Floer 同源性都有影响。特别是，我们证明某些多项式绝不是允许同源三球塞弗特纤维手术的结的亚历山大多项式。另一方面，弗洛尔结同调限制也适用于亚历山大多项式不提供信息的情况，例如木下-寺坂结。
We explore certain restrictions on knots in the three-sphere which admit non-trivial Seifert fibered surgeries. These restrictions stem from the Heegaard Floer homology for Seifert fibered spaces, and hence they have consequences for both the Alexander polynomial of such knots, and also their knot Floer homology. In particular, we show that certain polynomials are never the Alexander polynomials of knots which admit homology three-sphere Seifert fibered surgeries. The knot Floer homology restrictions, on the other hand, apply also in cases where the Alexander polynomial gives no information, such as the Kinoshita-Terasaka knots.