Satellite knots and L-space surgeries

TL;DR

This paper establishes conditions under which satellite knots can admit L-space surgeries and introduces new families of patterns that generate satellite L-space knots, advancing understanding in knot theory and 3-manifold topology.

Contribution

It provides new sufficient conditions for satellite knots to admit L-space surgeries and constructs infinite families of such knots using novel patterns.

Findings

Identified conditions for satellite knots to admit L-space surgeries

Constructed new infinite families of satellite L-space knots

Expanded the class of known L-space knots through pattern analysis

Abstract

We give sufficient conditions for a satellite knot to admit an L-space surgery, and use this result to give new infinite families of patterns which produce satellite L-space knots.