Width of the Whitehead double of a nontrivial knot

TL;DR

This paper establishes a precise relationship between the width of a nontrivial knot and its Whitehead double, showing that the width doubles in a specific way.

Contribution

The paper proves that the width of the Whitehead double of a nontrivial knot is exactly four times the width of the original knot, providing a clear quantitative link.

Findings

Width of Whitehead double is four times the original knot's width.

Provides a formula relating knot width and Whitehead doubles.

Advances understanding of knot invariants under Whitehead doubling.

Abstract

In this paper, we prove that $w(K) =4w(J)$, where $w(.)$ is the width of a knot and $K$ is the Whitehead double of a nontrivial knot $J$.