Ribbon concordance and the minimality of tight fibered knots

TL;DR

This paper proves that all tight fibered knots are minimal under ribbon concordance in the 3-sphere and provides a table of prime minimal knots up to 8 crossings, enhancing understanding of knot orderings.

Contribution

It establishes the minimality of tight fibered knots in the ribbon concordance partial order and compiles a comprehensive table of prime minimal knots up to 8 crossings.

Findings

All tight fibered knots are minimal in the ribbon concordance order.

A table of prime minimal knots up to 8 crossings is provided.

The exception for 8-crossing knots is noted for 8_{15}.

Abstract

Agol proved that ribbon concordance forms a partial ordering on the set of knots in the $3$-sphere. In this paper, we prove that all tight fibered knots are minimal in this partially ordered set. We also give the table of prime minimal knots up to $8$-crossings except for $8_{15}$.