A note on the sheet numbers of twist-spun knots

摘要

The sheet number of a 2-knot is a quantity which reflects the complexity of the knotting in 4-space. The aim of this note is to determine the sheet numbers of the 2- and 3-twist-spun trefoils. For this purpose, we give a lower bound of the sheet number by the quandle cocycle invariant of a 2-knot, and an upper bound by the crossing number of a 1-knot.