Apparent contours of stable maps into the sphere

Taishi Fukuda and Takahiro Yamamoto

Journal of Singularities
volume 3 (2011), 113-125

Received: 14 May 2010. Received in revised form: 9 June 2011.

DOI: 10.5427/jsing.2011.3g

Add a reference to this article to your citeulike library.


For a stable map φ:M → S^2 of a closed and connected surface into the sphere, let c(φ) and n(φ) denote the numbers of cusps and nodes respectively. In this paper, for each integer i ≥ 1, in the given homotopy class with i fold curve components, we will determine the minimal number c +n.


stable map, cusp, node, minimal contour, genus, mapping degree

Mathematical Subject Classification:

Primary: 57R45; Secondary: 57N13

Author(s) information:

Taishi Fukuda Takahiro Yamamoto
15-28-303, Fujimi 1-chome, Urayasu, Chiba Faculty of Engineering, Kyushu Sangyo University
279-0043 Japan 3-1, Matsukadai 2-chome, Higashi-ku, Fukuoka
813-8503 Japan
email: email: