The search for non-symmetric ribbon knots

TL;DR

This paper catalogs symmetric union presentations for ribbon knots with 11 and 12 crossings, identifies potential non-symmetric examples, and provides a comprehensive atlas of band diagrams for prime ribbon knots in this range.

Contribution

It offers the first extensive tabulation of symmetric union presentations and a complete atlas of band diagrams for prime ribbon knots with 11 and 12 crossings.

Findings

Tabulated symmetric union presentations for knots with 11 and 12 crossings

Identified potential ribbon knots not representable as symmetric unions

Provided a comprehensive atlas of band diagrams for prime ribbon knots

Abstract

We present the results of Axel Seeliger's tabulation of symmetric union presentations for ribbon knots with crossing numbers 11 and 12 and exhibit possible examples for ribbon knots which are not representable as symmetric unions. In addition, we give a complete atlas of band diagrams for prime ribbon knots with 11 and 12 crossings.