Geodesic
Apparent contours of stable maps of surfaces with boundary into the plane
Journal of Singularities, Tome 22 (2020), pp. 114-133

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Let M be a connected compact surface with boundary. A C^∞ map M -> R^2 is admissible if it is non-singular on a neighborhood of the boundary. For a C^∞ stable map f: M -> R^2, denote by c(f) and n(f), i(f) the number of cusps and nodes, connected components of the set of singular points respectively. In this paper, we introduce the notion of admissibly homotopic among C^∞ maps M -> R^2, and we will determine the minimal number c +n for each admissibly homotopy class.
DOI : 10.5427/jsing.2020.22h
Classification : 57R45, 57R35, 57R90, 58K65 
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     author = {Takahiro Yamamoto},
     title = {Apparent contours of stable maps of surfaces with boundary into the plane},
     journal = {Journal of Singularities},
     pages = {114--133},
     publisher = {mathdoc},
     volume = {22},
     year = {2020},
     doi = {10.5427/jsing.2020.22h},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.22h/}
}
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Takahiro Yamamoto. Apparent contours of stable maps of surfaces with boundary into the plane. Journal of Singularities, Tome 22 (2020), pp. 114-133. doi: 10.5427/jsing.2020.22h

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