Heegaard Floer homology and chirally cosmetic surgeries

Abstract: A pair of surgeries on a knot is chirally cosmetic if they result in homeomorphic manifolds with opposite orientations. We find new obstructions to the existence of such surgeries coming from Heegaard Floer homology; in particular, we make use of immersed curve formulations of knot Floer homology and the corresponding surgery formula. As an application, we completely classify chirallly cosmetic surgeries on odd alternating pretzel knots, and we rule out such surgeries for a large class of Whitehead doubles. Furthermore, we rule out cosmetic surgeries for L-space knots along slopes with opposite signs.