On the triple point number of surface-links in Yoshikawa's table
Geometric Topology
2022-05-24 v1
Abstract
Yoshikawa made a table of knotted surfaces in R^4 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 R^3 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.
Cite
@article{arxiv.2205.11120,
title = {On the triple point number of surface-links in Yoshikawa's table},
author = {Nicholas Cazet},
journal= {arXiv preprint arXiv:2205.11120},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2204.13860