Small Seifert fibered surgery on hyperbolic pretzel knots

TL;DR

This paper classifies all hyperbolic pretzel knots that admit Seifert fibered surgeries, completing the understanding of exceptional surgeries on these knots, and provides preliminary results for related Montesinos knots.

Contribution

It finalizes the classification of hyperbolic pretzel knots with Seifert fibered surgeries and advances understanding of surgeries on non-pretzel Montesinos knots.

Findings

Complete classification of hyperbolic pretzel knots with Seifert fibered surgeries

Identification of exceptional surgeries on these knots

Initial results for non-pretzel Montesinos knots

Abstract

We complete the classification of hyperbolic pretzel knots admitting Seifert fibered surgeries. This is the final step in understanding all exceptional surgeries on hyperbolic pretzel knots. We also present results toward similar classifications for non-pretzel Montesinos knots of length three.