Apparent contours of stable maps between closed surfaces

Abstract

Let M and N be connected and orientable, closed surfaces. For a stable map φ : M → N, denote by c(φ) and n(φ) the numbers of cusps and nodes of φ respectively. In this paper, we determine the minimal number c(φ) + n(φ) among the apparent contours of degree d stable maps M → N whose singular points set consists of one component.