S³上结的Dehn手术

What's Next? Pub Date : 2014-07-02 DOI:10.2307/j.ctvthhdvv.14

Yi Ni, Xingru Zhang

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引用次数: 0

摘要

我们证明了在S中的非三叶结上通过Dehn手术可以得到6个Nil Seifert纤维空间，其中{60,144,156,288,300}是所有这些手术的精确集合，这些手术可以得到结的镜像。我们推测S中有4个特定的双曲节，可以进行无纤维手术。我们也给出了关于S型双曲结的Seifert纤维手术的一些更一般的结果和一个更一般的猜想。

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Dehn Surgery on Knots in S³ Producing Nil Seifert Fibered Spaces

We prove that there are exactly 6 Nil Seifert fibred spaces which can be obtained by Dehn surgeries on non-trefoil knots in S, with {60, 144, 156, 288, 300} as the exact set of all such surgery slopes up to taking the mirror images of the knots. We conjecture that there are exactly 4 specific hyperbolic knots in S which admit Nil Seifert fibred surgery. We also give some more general results and a more general conjecture concerning Seifert fibred surgeries on hyperbolic knots in S.

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