Infinite families of non-fibered twisted torus knots

TL;DR

This paper constructs infinite families of twisted torus knots that are not fibered by analyzing their Alexander polynomials, demonstrating that their leading coefficients can be arbitrary integers.

Contribution

It provides explicit formulas and infinite examples of non-fibered twisted torus knots based on Alexander polynomial analysis.

Findings

Infinite families of non-fibered twisted torus knots constructed.

Leading coefficients of Alexander polynomials can be arbitrary integers.

Demonstrates the non-fibered property through polynomial analysis.

Abstract

We present explicit infinite families of twisted torus knots that are not fibered. Our approach relies on an explicit formula for the Alexander polynomial derived in our previous work. We show that the leading coefficients of the Alexander polynomials of twisted torus knots can take arbitrary integer values, which immediately yields infinitely many examples of non-fibered twisted torus knots.