Fibered and primitive/Seifert twisted torus knots

2011/11/07 by Doleshal, Brandy Guntel
#57M25 #57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1111.1696

Abstract

The twisted torus knots lie on the standard genus 2 Heegaard surface for S³, as do the primitive/primitive and primitive/Seifert knots. It is known that primitive/primitive knots are fibered, and that not all primitive/Seifert knots are fibered. Since there is a wealth of primitive/Seifert knots that are twisted torus knots, we consider the twisted torus knots to partially answer the question of which primitive/Seifert knots are fibered. A braid computation shows that a particular family of twisted torus knots is fibered, and that computation is then used to generalize the results of a previous paper by the author.

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• Seifert fibered surgeries on strongly invertible knots without primitive/Seifert positions
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