Note on the distortion of (2,q)-torus knots

TL;DR

This paper demonstrates that the distortion of (2,q)-torus knots cannot be bounded below by a linear function, indicating unbounded complexity in their geometric embedding.

Contribution

It reveals that the distortion of (2,q)-torus knots is not linearly bounded from below, providing new insights into their geometric properties.

Findings

Distortion of (2,q)-torus knots is unbounded from below.

Linear bounds do not apply to the distortion of these knots.

The result impacts understanding of knot complexity and embedding distortions.

Abstract

We show that the distortion of the (2,q)-torus knot is not bounded linearly from below.