Fibered and primitive/Seifert twisted torus knots

TL;DR

This paper investigates which primitive/Seifert twisted torus knots are fibered, using braid computations to identify a family of fibered knots and generalize previous results in the field.

Contribution

It introduces a new family of fibered primitive/Seifert twisted torus knots and extends prior findings through braid computation techniques.

Findings

A specific family of twisted torus knots is fibered.

Braid computations can determine fiberedness of these knots.

Results generalize previous work on primitive/Seifert knots.

Abstract

The twisted torus knots lie on the standard genus 2 Heegaard surface for $S^3$, 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.