Minimal bridge projections for 11-crossing prime knots

TL;DR

This paper determines the minimal bridge projections and indices for all 11-crossing prime knots, revealing that most non-rational, non-Montesinos knots have a bridge index of three.

Contribution

It provides the first comprehensive set of minimal bridge projections and indices for 11-crossing prime knots, including explicit minimal representations.

Findings

All non-rational, non-Montesinos 11-crossing prime knots have bridge index three.

Explicit minimal bridge projections are provided for each of these knots.

The bridge indices for these knots are summarized effectively in the paper.

Abstract

We give the bridge indices for 11-crossing prime knots and give a minimal bridge projection for each of these knots. The results on the indices may be easily summarized: all of these knots that are not rational knots or Montesinos knots have bridge index three.