The bridge index and the braid index for twist positive knots

TL;DR

This paper proves that for twist positive knots, the bridge index equals the braid index, using knot Floer torsion order, addressing a conjecture related to these knot invariants.

Contribution

It establishes the equality of bridge and braid indices for twist positive knots, advancing understanding of their relationship and providing a proof for a specific class of knots.

Findings

Bridge index equals braid index for twist positive knots

Uses knot Floer torsion order to prove the result

Addresses a conjecture by Krishna and Morton

Abstract

In general, the bridge index of a knot is less than or equal to its braid index. A natural question is when these two values coincide. Motivated by a conjecture of Krishna and Morton, we prove that the bridge index and the braid index coincide for all twist positive knots, using the knot Floer torsion order. Here, a twist positive knot is a knot that admits a positive braid representative containing at least one full twist.