Minimal triple point numbers of some non-orientable surface-links

Abstract

An embedded surface in R4 is projected into R3 with the double point set which includes a finite number of triple points. We consider the minimal number of such triple points among all projections of embedded surfaces which are ambient isotopic to a given surface and show that for any non-negative integer N there exists a 2-component non-orientable surface in R4 whose minimal triple point number is equal to 2N.