Research ArticleNo Access

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

Nicholas Cazet

University of California at Davis, 1 Shields Ave., Davis, CA 95616, USA

https://doi.org/10.1142/S0218216523500372Cited by:0 (Source: Crossref)

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-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.

Keywords:

AMSC: 57K45

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