2018/04/25 by András Juhász, Juhász, András, Ian Zemke +1 · 2 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT
paper · pdf · doi:10.48550/arxiv.1804.09589
13 pages, 3 figures, to appear in Selecta Mathematica
arxiv created 2019/12/10 · arxiv updated 2019/12/12
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.