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Distinguishing slice disks using knot Floer homology

Research paper by András Juhász, Ian Zemke

Indexed on: 21 Dec '19Published on: 21 Dec '19Published in: Selecta Mathematica



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.