Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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EXAMPLES OF KNOTS IN S3 ADMITTING SEIFERT-FIBERED SURGERIES OVER S2 WITH FOUR EXCEPTIONAL FIBERS

  • Kang, Sungmo (Department of Mathematics Education, Chonnam National University)
  • Received : 2018.06.07
  • Accepted : 2018.06.25
  • Published : 2018.09.25
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Abstract

In [4] Miyazaki and Motegi constructed one family of knots in $S^3$ which admits Dehn surgery producing a Seifert-fibered space over $S^2$ with four exceptional fibers. On the other hand, in [3] using doubly hyper Seifert twisted torus knots, the author constructed six families of knots in $S^3$ which admit Dehn surgery yielding a Seifert-fibered space over $S^2$ with four exceptional fibers. It is questioned in [3] whether or not the family of the knots constructed in [4] belongs to one of the six families of the knots in [3]. In this paper, we give the positive answer for this question.

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References

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  2. J. Kalliongis and C. M. Tsau, Seifert fibered surgery manifolds of composite knots, Proc. Amer. Math. Soc., 108 (1990), 1047-1053. https://doi.org/10.1090/S0002-9939-1990-1002161-6
  3. S. Kang, Knots admitting Seifert-fibered surgeries over $S^2$ with four exceptional fibers, Bull. Korean Math. Soc., 52(1) (2015), 313-321. https://doi.org/10.4134/BKMS.2015.52.1.313
  4. K. Miyazaki and K. Motegi, Seifert fibered manifolds and Dehn surgery, Topology 36(2) (1997), 579-603. https://doi.org/10.1016/0040-9383(96)00009-2