On the slice genus of quasipositive knots in indefinite 4-manifolds

• David Baraglia ^[1]
  1. [1] University of Adelaide

     University of Adelaide

     Australia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 4, 2023
• Idioma: inglés
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• Resumen

  • Let X be a closed indefinite 4-manifold with b+(X) = 3 (mod 4) and with nonvanishing mod 2 Seiberg–Witten invariants. We prove a new lower bound on the genus of a properly embedded surface in X\B4 representing a given homology class and with boundary a quasipositive knot K ⊂ S3. In the null-homologous case our inequality implies that the minimal genus of such a surface is equal to the slice genus of K. If X is symplectic then our lower bound differs from the minimal genus by at most 1 for any homology class that can be represented by a symplectic surface. Along the way, we also prove an extension of the adjunction inequality for closed 4-manifolds to classes of negative self-intersection without requiring X to be of simple type.