On the triple point number of surface-links in Yoshikawa’s table

Abstract

Yoshikawa made a table of knotted surfaces in [Formula: see text] with ch-index 10 or less. This remarkable table is the first to enumerate knotted surfaces analogous to the classical prime knot table. A broken sheet diagram of a surface-link is a generic projection of the surface in [Formula: see text] with crossing information along its singular set. The minimal number of triple points among all broken sheet diagrams representing a given surface-link is its triple point number. This paper compiles the known triple point numbers of the surface-links represented in Yoshikawa’s table and calculates or provides bounds on the triple point number of the remaining surface-links.