Geodesic
Apparent contours of stable maps into the sphere
Journal of Singularities, Tome 3 (2011), pp. 113-125

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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.
DOI : 10.5427/jsing.2011.3g
Classification : :57R45, :57N13 
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     author = {Taishi Fukuda and Takahiro Yamamoto},
     title = {Apparent contours of stable maps into the sphere},
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     publisher = {mathdoc},
     volume = {3},
     year = {2011},
     doi = {10.5427/jsing.2011.3g},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2011.3g/}
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Taishi Fukuda; Takahiro Yamamoto. Apparent contours of stable maps into the sphere. Journal of Singularities, Tome 3 (2011), pp. 113-125. doi: 10.5427/jsing.2011.3g

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