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 $\mathrm{SU}<!--FUNCTION\; APPLICATION-->(2)$ representations of fundamental groups of Dehn surgeries.

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