Dehn surgery on knots in $S^3$ producing Nil Seifert fibred spaces

Yi Ni; Xingru Zhang

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arXiv · 1407.0648

Dehn surgery on knots in $S^3$ producing Nil Seifert fibred spaces

Yi Ni·Xingru Zhang

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Abstract

We prove that there are exactly $6$ Nil Seifert fibred spaces which can be obtained by Dehn surgeries on non-trefoil knots in $S^3$, 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 $S^3$ 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 $S^3$.

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BibTeX RIS

Yi Ni, Xingru Zhang. 2014-07-02. Dehn surgery on knots in $S^3$ producing Nil Seifert fibred spaces. https://arxiv.org/abs/1407.0648

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