Seifert fibered surgery and Rasmussen invariant

TL;DR

This paper introduces a new criterion based on the Rasmussen invariant and signature to identify Montesinos knots and applies it to prove that certain pretzel knots do not admit Seifert fibered surgeries.

Contribution

It provides a novel criterion for recognizing Montesinos knots and demonstrates its application in ruling out Seifert fibered surgeries on specific pretzel knots.

Findings

A new criterion for Montesinos knots using Rasmussen invariant and signature.

Certain $(p,q,q)$-pretzel knots with $p,q geq 2$ do not admit Seifert fibered surgeries.

Enhanced understanding of the relationship between knot invariants and Seifert fibered surgeries.

Abstract

We give a new criterion for a given knot to be a Montesinos knot by using the Rasmussen invariant and the signature. We apply the criterion to study Seifert fibered surgery on a strongly invertible knot, and show that a $(p,q,q)$-pretzel knot with integers $p,q \ge 2$ admits no Seifert fibered surgery.