  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.
