Distinguishing slice disks using knot Floer homology

András Juhász, Ian Zemke

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Article number5
JournalSelecta Mathematica, New Series
Volume26
Issue number1
DOIs
StatePublished - Feb 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

Keywords

  • 4-manifold
  • Concordance
  • Heegaard Floer homology
  • Slice disk

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