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Correction terms and the nonorientable slice genus. (English) Zbl 1458.57006
Summary: 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 J. Batson [Math. Res. Lett. 21, No. 3, 423–436 (2014; Zbl 1308.57004)] and coincides with Ozsváth–Stipsicz–Szabó’s bound [P. S. Ozsváth et al., Int. Math. Res. Not. 2017, No. 17, 5137–5181 (2017; Zbl 1405.57024)] 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 \(\gamma_{4}(K)\).

MSC:
57K10 Knot theory
57K18 Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.)
57R58 Floer homology
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