Pretzel knots with L-space surgeries

TL;DR

This paper classifies pretzel knots that admit L-space surgeries, expanding understanding of which knots produce three-manifolds with minimal Heegaard Floer homology, based on Gabai's classification of fibered pretzel links.

Contribution

It provides a complete classification of pretzel knots with any number of tangles that admit L-space surgeries, utilizing Gabai's fibered link classification.

Findings

Identifies all pretzel knots with L-space surgeries

Uses Gabai's classification to determine fibered pretzel links

Advances understanding of Heegaard Floer homology in knot theory

Abstract

A rational homology sphere whose Heegaard Floer homology is the same as that of a lens space is called an L-space. We classify pretzel knots with any number of tangles which admit L-space surgeries. This rests on Gabai's classification of fibered pretzel links.