Hyperbolic, L-space knots and exceptional Dehn surgeries

TL;DR

This paper presents an example of a hyperbolic L-space knot that admits no exceptional Dehn surgeries, including Seifert fibered surgeries, highlighting new phenomena in the study of knot surgeries.

Contribution

It provides a concrete example of a hyperbolic L-space knot with no exceptional surgeries, expanding understanding of the diversity of L-space knots.

Findings

The example is hyperbolic and admits no Seifert fibered surgeries.

It demonstrates that not all L-space knots have exceptional surgeries.

The result contrasts with known classes like torus and Berge knots.

Abstract

A knot in the 3-sphere is called an L--space knot if it admits a nontrivial Dehn surgery yielding an L--space. Like torus knots and Berge knots, many L--space knots admit also a Seifert fibered surgery. We give a concrete example of a hyperbolic, L-space knot which has no exceptional surgeries, in particular, no Seifert fibered surgeries.