Meridional rank of whitehead doubles

TL;DR

This paper proves that for a broad class of knots called algebraically tame knots, the meridional rank and bridge number of their Whitehead doubles are equal, extending understanding of their topological properties.

Contribution

It establishes the equality of meridional rank and bridge number for Whitehead doubles of algebraically tame knots, a significant generalization beyond previous specific cases.

Findings

Meridional rank equals bridge number for Whitehead doubles of algebraically tame knots.

Algebraically tame knots include torus and iterated cable knots.

The result broadens the class of knots with known meridional rank and bridge number relationship.

Abstract

We prove that the meridional rank and the bridge number of the Whitehead double of a prime algebraically tame knot coincide. Algebraically tame knots are a broad generalization of torus knots and iterated cable knots.