  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.
