Obstructing Reducible Surgeries: Slice Genus and Thickness Bounds

In this paper, we study reducible surgeries on knots in S3. We develop thickness bounds for L-space knots that admit reducible surgeries and lower bounds on the slice genus for general knots that admit reducible surgeries. The lower bound on thickness for L-space knots allows us to finish off the verification of the cabling conjecture for thin knots, which was mostly worked out in [DeY21]. We also provide a new upper bound on reducing slopes for fibered, hyperbolic slice knots and on multiple reducing slopes for slice knots. Our techniques involve the d-invariants and mapping cone formula from Heegaard Floer homology.