Distinguishing slice disks using knot Floer homology

• András Juhász ^[1] ; Ian Zemke ^[2]
  1. [1] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
  2. [2] Princeton University

     Princeton University

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 1, 2020
• Idioma: inglés
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• Resumen

  • We study the classification of slice disks of knots up to isotopy and diffeomorphism using an invariant in knot Floer homology. We compute the invariant of a slice disk obtained by deform-spinning, and show that it can be effectively used to distinguish non-isotopic slice disks with diffeomorphic complements. Given a slice disk of a composite knot, we define a numerical stable diffeomorphism invariant called the rank. This can be used to show that a slice disk is not a boundary connected sum, and to give lower bounds on the complexity of certain hyperplane sections of the slice disk.