L-space knots are fibered and strongly quasipositive

TL;DR

This paper presents a simpler proof that L-space knots are fibered and strongly quasipositive, using less Heegaard Floer machinery, enabling generalization to other Floer homologies like instanton Floer homology.

Contribution

It provides a new, more accessible proof of a key property of L-space knots, facilitating extensions to other Floer homology theories.

Findings

L-space knots are fibered and strongly quasipositive

The proof can be adapted to instanton Floer homology

Generalizes results on $SU(2)$ representations of fundamental groups

Abstract

We give a new, conceptually simpler proof of the fact that knots in $S^3$ with positive L-space surgeries are fibered and strongly quasipositive. Our motivation for doing so is that this new proof uses comparatively little Heegaard Floer-specific machinery and can thus be translated to other forms of Floer homology. We carried this out for instanton Floer homology in our recent article "Instantons and L-space surgeries", and used it to generalize Kronheimer and Mrowka's results on $SU(2)$ representations of fundamental groups of Dehn surgeries.