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

Nicholas Cazet

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arXiv · 2205.11120

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

Nicholas Cazet

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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.

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Nicholas Cazet. 2022-05-23. On the triple point number of surface-links in Yoshikawa's table. https://arxiv.org/abs/2205.11120

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