PRIMITIVE/SEIFERT KNOTS WHICH ARE NOT TWISTED TORUS KNOT POSITION

• 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;

Abstract
The twisted torus knots and the primitive/Seifert knots both lie on a genus 2 Heegaard surface of $\small{S^3}$. 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.
Keywords
knots;twisted torus knots;primitive curves;Seifert curves;proper power curves;primitive/Seifert knots;
Language
English
Cited by
References
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