Constructing generic smooth maps of a manifold into a surface with prescribed singular loci
Annales de l'Institut Fourier, Volume 45 (1995) no. 4, p. 1135-1162

It is known that the singular set S(f) of a generic smooth map f:MN of an n-dimensional manifold into a surface is a closed 1-dimensional submanifold of M and that it has a natural stratification induced by the absolute index. In this paper, we give a complete characterization of those 1-dimensional (stratified) submanifolds which arise as the singular set of a generic map in terms of the homology class they represent.

On sait que l’ensemble des points singuliers S(f) d’une application différentiable générique f:MN d’une variété à n dimensions dans une surface est une sous-variété à une dimension de M et que S(f) a une stratification naturelle introduite par l’indice absolu. Dans cet article nous donnons une caractérisation complète des sous-variétés à une dimension (stratifiées) qui se présentent comme un ensemble de points singuliers d’une application générique, en termes de classes d’homologie représentées par les sous-variétés.

@article{AIF_1995__45_4_1135_0,
     author = {Saeki, Osamu},
     title = {Constructing generic smooth maps of a manifold into a surface with prescribed singular loci},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {45},
     number = {4},
     year = {1995},
     pages = {1135-1162},
     doi = {10.5802/aif.1489},
     zbl = {0833.57018},
     mrnumber = {97e:57035},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1995__45_4_1135_0}
}
Saeki, Osamu. Constructing generic smooth maps of a manifold into a surface with prescribed singular loci. Annales de l'Institut Fourier, Volume 45 (1995) no. 4, pp. 1135-1162. doi : 10.5802/aif.1489. http://www.numdam.org/item/AIF_1995__45_4_1135_0/

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