Correction Terms and the Nonorientable Slice Genus

Source abstract

By considering negative surgeries on a knot K in S3, we derive a lower bound on the nonorientable slice genus γ4(K) in terms of the signature σ(K) and the concordance invariants Vi(K¯); this bound strengthens a previous bound given by Batson and coincides with Ozsváth–Stipsicz–Szabó’s bound in terms of their υ invariant for L-space knots and quasi-alternating knots. A curious feature of our bound is superadditivity, implying, for instance, that the bound on the stable nonorientable slice genus is sometimes better than that on γ4(K).