Seifert fibered surgeries on strongly invertible knots without primitive/Seifert positions

TL;DR

This paper constructs an infinite family of Seifert fibered surgeries on strongly invertible knots that lack primitive/Seifert positions, expanding understanding of knot surgeries beyond known configurations.

Contribution

It introduces a new family of knots obtained via twists on seiferters, demonstrating they do not admit primitive/Seifert positions, unlike previously studied cases.

Findings

Infinite family of such knots constructed

These knots are derived from trefoil knots with specific twists

They lack primitive/Seifert positions, contrary to common cases

Abstract

We find an infinite family of Seifert fibered surgeries on strongly invertible knots which do not have primitive/Seifert positions. Each member of the family is obtained from a trefoil knot after alternate twists along a pair of seiferters for a Seifert fibered surgery on a trefoil knot.