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

2022/05/23 by Cazet, Nicholas
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2205.11120

Abstract

Yoshikawa made a table of knotted surfaces in R⁴ 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 R³ with crossing information along its singular set. The minimal number of triple points among all broken sheet diagrams representing a given surface-knot 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.

Related

• Estimating the Kirby--Thompson Invariants of Surface-Links in the Yoshikawa Table
• On surface-knots with triple point number at most three
• Trisected Rainbows and Braids
• The triple point number of surface-knots of genus one is at least four
• Tri-plane diagrams for simple surfaces in S⁴