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PRIMITIVE/SEIFERT KNOTS WHICH ARE NOT TWISTED TORUS KNOT POSITION
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  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 4,  2013, pp.775-791
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.4.775
 Title & Authors
PRIMITIVE/SEIFERT KNOTS WHICH ARE NOT TWISTED TORUS KNOT POSITION
Kang, Sungmo;
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 Abstract
The twisted torus knots and the primitive/Seifert knots both lie on a genus 2 Heegaard surface of . 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.
 Keywords
knots;twisted torus knots;primitive curves;Seifert curves;proper power curves;primitive/Seifert knots;
 Language
English
 Cited by
 References
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J. Berge, A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody, arXiv:0910.3038

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J. Berge, Private communication, (2012).

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J. Dean, Small Seifert-fibered Dehn surgery on hyperbolic knots, Algebraic and Geometric Topology 3 (2003), 435-472. crossref(new window)

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R. P. Osborne and R. S. Stevens, Group Presentations Corresponding to Spines of 3-Manifolds II, Trans. Amer. Math. Soc. 234 (1977), 213-243.

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H. Zieschang, On Heegaard Diagrams of 3-Manifolds, Asterisque 163-164 (1988), 247-280.