2020/03/05 by Hom, Jennifer, Kang, Sungkyung, Park, JungHwan · 1 citation
#57K10 #57K18 #57K40 #FOS: Mathematics #Geometric Topology (math.GT) #and 57N70
paper · doi:10.48550/arxiv.2003.02832
The fusion number of a ribbon knot is the minimal number of 1-handles needed to construct a ribbon disk. The strong homotopy fusion number of a ribbon knot is the minimal number of 2-handles in a handle decomposition of a ribbon disk complement. We demonstrate that these invariants behave completely differently under cabling by showing that the (p,1)-cable of any ribbon knot with fusion number one has strong homotopy fusion number one and fusion number p. Our main tools are Juhász-Miller-Zemke's bound on fusion number coming from the torsion order of knot Floer homology and Hanselman-Watson's cabling formula for immersed curves.