Fibered ribbon pretzels

TL;DR

This paper classifies fibered ribbon pretzel knots up to mutation using lattice embeddings and Gabai's classification, providing a comprehensive understanding with some exceptions.

Contribution

It offers a complete classification of fibered ribbon pretzel knots up to mutation, combining lattice techniques with existing knot theory classifications.

Findings

Classification is complete except for certain exceptional cases.

Uses lattice embedding techniques to analyze knot fiberedness.

Identifies ribbon disks outside standard pretzel patterns.

Abstract

We classify fibered ribbon pretzel knots up to mutation. The classification is complete, except perhaps for members of Lecuona's ``exceptional'' family of [Lec15]. The result is obtained by combining lattice embedding techniques with Gabai's classification of fibered pretzel knots, and exhibiting ribbon disks, some of which lie outside of known patterns for standard pretzel projections.