An estimate of the triple point numbers of surface-knots by quandle cocycle invariants
A surface knot is a closed 2 manifold embedded in \(\mathbb{R}^4\), considered up to ambient isotopy; surface knots are represented by surface knot diagrams, i.e. immersed surfaces in \(\mathbb{R}^3\) with singular set enhanced to show crossing information. This singular set consists of a union of simple closed curves and arcs which may intersect in a number of triple points. The triple point number of a surface knot \(K\) is the minimal number of triple points over all diagrams of \(K\); it is analagous to the crossing number for ordinary knots. In this paper, the author establishes a lower bound on the triple point number of oriented surface knots which have nontrival values of quandle 3-cocyle invariants over the dihedral quandle \(R_5\).
scientific article; zbMATH DE number 2092794
scientific article