Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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PRIMITIVE/SEIFERT KNOTS WHICH ARE NOT TWISTED TORUS KNOT POSITION

  • Kang, Sungmo (Department of Mathematics Education, Chonnam National University)
  • Received : 2013.11.05
  • Accepted : 2013.11.19
  • Published : 2013.12.25
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Abstract

The twisted torus knots and the primitive/Seifert knots both lie on a genus 2 Heegaard surface of $S^3$. In [5], J. Dean used the twisted torus knots to provide an abundance of examples of primitive/Seifert knots. Also he showed that not all twisted torus knots are primitive/Seifert knots. In this paper, we study the other inclusion. In other words, it shows that not all primitive/Seifert knots are twisted torus knot position. In fact, we give infinitely many primitive/Seifert knots that are not twisted torus knot position.

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References

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