A note on band surgery and the signature of a knot

Band surgery is an operation relating pairs of knots or links in the three-sphere. We prove that if two quasi-alternating knots K and K ′ of the same square-free determinant are related by a band surgery, then the absolute value of the difference in their signatures is either 0 or 8. This obstruction follows from a more general theorem about the difference in the Heegaard Floer d-invariants for pairs of L-spaces that are related by distance one Dehn fillings and satisfy a certain condition in first homology. These results imply that T ( 2 , 5 ) is the only torus knot T ( 2 , m ) with m square-free that admits a chirally cosmetic banding, that is, a band surgery operation to its mirror image. We conclude with a discussion on the scarcity of chirally cosmetic bandings.