## The Michigan Mathematical Journal

### 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 $\gamma_{4}(K)$ in terms of the signature $\sigma(K)$ and the concordance invariants $V_{i}(\overline {K})$; 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 $\gamma_{4}(K)$.

#### Article information

Source
Michigan Math. J., Volume 67, Issue 1 (2018), 59-82.

Dates
Revised: 1 February 2017
First available in Project Euclid: 29 November 2017

https://projecteuclid.org/euclid.mmj/1511924604

Digital Object Identifier
doi:10.1307/mmj/1511924604

Mathematical Reviews number (MathSciNet)
MR3770853

Zentralblatt MATH identifier
06965589

#### Citation

Golla, Marco; Marengon, Marco. Correction Terms and the Nonorientable Slice Genus. Michigan Math. J. 67 (2018), no. 1, 59--82. doi:10.1307/mmj/1511924604. https://projecteuclid.org/euclid.mmj/1511924604

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