Positive links are strongly quasipositive
Positive links are strongly quasipositive
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正向链接是强准正向的
DOI：
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发表时间：
1998
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通讯作者：
L. Rudolph
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作者：
L. Rudolph
设S（D）是通过将塞弗特算法应用于有向链路图D而产生的曲面。证明了若D没有负交叉，则S（D）是拟正的Seifert曲面，即S（D）不可压缩地嵌入在由正的Hopf环垂直的纤维曲面上.这个结果，结合“局部托姆猜想”的真实性，有各种有趣的结果;例如，它产生了一个容易计算的估计的切片eeternity特征的链接L（D）（其中D是任意的），扩展和经常改善“切片- Bennequin不等式”的封闭编织图;它导致了另一个证明的手征性的积极和几乎积极的结。AMS分类57 M25; 32 S55，14 H99
Let S(D) be the surface produced by applying Seifert’s algorithm to the oriented link diagram D. I prove that if D has no negative crossings then S(D) is a quasipositive Seifert surface, that is, S(D) embeds incompressibly on a fiber surface plumbed from positive Hopf annuli. This result, combined with the truth of the “local Thom Conjecture”, has various interesting consequences; for instance, it yields an easily-computed estimate for the slice euler characteristic of the link L(D) (where D is arbitrary) that extends and often improves the “slice– Bennequin inequality” for closed-braid diagrams; and it leads to yet another proof of the chirality of positive and almost positive knots. AMS Classification 57M25; 32S55, 14H99