Danceability, Directed by Braid Index

TL;DR

This paper introduces a new danceability knot invariant inspired by Schaffer's concept, demonstrating that it is bounded above by the braid index, thus linking knot danceability to braid theory.

Contribution

The paper develops a novel danceability invariant for knots and establishes its relationship with the braid index, expanding the theoretical framework of knot invariants.

Findings

Danceability invariant is bounded above by the braid index.

New connection between knot danceability and braid theory.

Extension of Schaffer's original danceability concept.

Abstract

Schaffer introduced the concept of danceability of a knot diagram. In this paper, we expand upon Schaffer's ideas to create a danceability knot invariant and show that this invariant is bounded above by the braid index.