Seifert fibered surgery on Montesinos knots

TL;DR

This paper classifies Seifert fibered surgeries on Montesinos knots of length 3, identifying a finite list of such surgeries and conjecturing its completeness, advancing understanding of exceptional Dehn surgeries.

Contribution

It provides a finite classification of Seifert fibered surgeries on length 3 Montesinos knots and presents a conjecture on the completeness of this list.

Findings

Identified 20 specific surgeries that are Seifert fibered.

Proved that only finitely many Seifert fibered surgeries exist for these knots.

Conjectured the list of surgeries is complete.

Abstract

Exceptional Dehn surgeries on arborescent knots have been classified except for Seifert fibered surgeries on Montesinos knots of length 3. There are infinitely many of them as it is known that 4n+6 and 4n+7 surgeries on a (-2, 3, 2n+1) pretzel knot are Seifert fibered. It will be shown that there are only finitely many others. A list of 20 surgeries will be given and proved to be Seifert fibered. We conjecture that this is a complete list.