Correction Terms and the Nonorientable Slice Genus

Abstract

By considering negative surgeries on a knot $K$ in $S^3$, we derive a lower bound on the nonorientable slice genus ${\gamma }_4\left(K\right)$ in terms of the signature $\sigma \left(K\right)$ and the concordance invariants $V_i\left(\overline{K}\right)$; this bound strengthens a previous bound given by Batson and coincides with Ozsváth–Stipsicz–Szabó’s bound in terms of their $\upsilon$ 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 ${\gamma }_4\left(K\right)$.