The Michigan Mathematical Journal

Correction Terms and the Nonorientable Slice Genus

Marco Golla and Marco Marengon

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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).

Article information

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

Received: 8 August 2016
Revised: 1 February 2017
First available in Project Euclid: 29 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 52R58


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.

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  • [1] P. Aceto and M. Golla, Dehn surgeries and rational homology balls, Alg. Geom. Topol. 17 (2017), 487–527.
  • [2] J. Batson, Nonorientable slice genus can be arbitrarily large, Math. Res. Lett. 21 (2014), no. 3, 423–436.
  • [3] J. Batson, Obstructions to slicing knots and splitting links, Ph.D. thesis, MIT, 2014.
  • [4] S. Behrens and M. Golla, Heegaard Floer correction terms, with a twist, Quantum Topol. 9 (2018), no. 1, 1–37.
  • [5] J. Bodnár, D. Celoria, and M. Golla, A note on cobordisms of algebraic knots, Algebr. Geom. Topol. 17 (2017), no. 4, 2543–2564.
  • [6] M. Borodzik and M. Hedden, The $\upsilon$ function of L-space knots is a Legendre transform, Math. Proc. Cambridge (2017, to appear), arXiv:1505.06672.
  • [7] M. Borodzik and C. Livingston, Heegaard Floer homology and rational cuspidal curves, Forum Math. Sigma 2 (2014), e28.
  • [8] F. Deloup and G. Massuyeau, Quadratic functions and complex spin structures on three-manifolds, Topology 44 (2005), no. 3, 509–555.
  • [9] C. McA. Gordon, R. A. Litherland, On the signature of a link, Invent. Math. 47 (1978), no. 1, 53–69.
  • [10] M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17 (1923), no. 1, 228–249.
  • [11] J. Hom and Z. Wu, Four-ball genus and a refinement of the Ozsváth–Szabó tau-invariant, J. Symp. Geom. 14 (2016), 305–323.
  • [12] D. Krcatovich, The reduced knot Floer complex, Topology Appl. 194 (2015), 171–201.
  • [13] A. S. Levine, D. Ruberman, and S. Strle, Non-orientable surfaces in homology cobordisms, Geom. Topol. 19 (2015), no. 1, 439–494, with an appendix by Ira M. Gessel.
  • [14] T. Lidman, On the infinity flavor of Heegaard Floer homology and the integral cohomology ring, Comment. Math. Helv. 88 (2013), no. 4, 875–898.
  • [15] Y. Ni and Z. Wu, Cosmetic surgeries on knots in $S^{3}$, J. Reine Angew. Math. 2015 (2015), no. 706, 1–17.
  • [16] P. S. Ozsváth, A. I. Stipsicz, and Z. Szabó, Concordance homomorphisms from knot Floer homology, Adv. Math. 315 (2017), 366–426.
  • [17] P. S. Ozsváth, A. I. Stipsicz, and Z. Szabó, Unoriented knot Floer homology and the unoriented four-ball genus, Int. Math. Res. Notices 17 (2017), 5137–5181.
  • [18] P. S. Ozsváth and Z. Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003), no. 2, 179–261.
  • [19] P. S. Ozsváth and Z. Szabó, Knot Floer homology and integer surgeries, Algebr. Geom. Topol. 8 (2008), no. 1, 101–153.
  • [20] J. A. Rasmussen, Lens space surgeries and a conjecture of Goda and Teragaito, Geom. Topol. 8 (2004), no. 3, 1013–1031.