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L-space knots are fibered and strongly quasipositive

### John A. Baldwin and Steven Sivek

Vol. 5 (2022), No. 1, 81–94
##### 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 article “Instantons and L-space surgeries” and used it to generalize Kronheimer and Mrowka’s results on $\mathrm{SU}\left(2\right)$ representations of fundamental groups of Dehn surgeries.

##### Keywords
L-spaces, Dehn surgery, Heegaard Floer homology
##### Mathematical Subject Classification
Primary: 57R58
Secondary: 57K18, 57K31