Superbridge and Bridge Indices for Knots

TL;DR

This paper establishes a tighter upper bound on the superbridge index of a knot based on its bridge index, refining previous estimates to better understand knot complexity.

Contribution

It provides an improved upper bound for the superbridge index in terms of the bridge index, advancing the mathematical understanding of knot invariants.

Findings

Upper bound on superbridge index improved to 3b - 1

Refinement from previous bound of 5b - 3

Enhances understanding of relationships between knot invariants

Abstract

We improve the upper bound on the superbridge index $sb[K]$ of a knot type $[K]$ in terms of the bridge index $b[K]$ from $sb[K] \leq 5b -3$ to $sb[K]\leq 3b[k] - 1$.