It is known that the singular set of a generic smooth map of an -dimensional manifold into a surface is a closed 1-dimensional submanifold of 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 d’une application différentiable générique d’une variété à dimensions dans une surface est une sous-variété à une dimension de et que 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},
pages = {1135--1162},
year = {1995},
publisher = {Association des Annales de l'Institut Fourier},
volume = {45},
number = {4},
doi = {10.5802/aif.1489},
mrnumber = {97e:57035},
zbl = {0833.57018},
language = {en},
url = {https://www.numdam.org/articles/10.5802/aif.1489/}
}
TY - JOUR AU - Saeki, Osamu TI - Constructing generic smooth maps of a manifold into a surface with prescribed singular loci JO - Annales de l'Institut Fourier PY - 1995 SP - 1135 EP - 1162 VL - 45 IS - 4 PB - Association des Annales de l'Institut Fourier UR - https://www.numdam.org/articles/10.5802/aif.1489/ DO - 10.5802/aif.1489 LA - en ID - AIF_1995__45_4_1135_0 ER -
%0 Journal Article %A Saeki, Osamu %T Constructing generic smooth maps of a manifold into a surface with prescribed singular loci %J Annales de l'Institut Fourier %D 1995 %P 1135-1162 %V 45 %N 4 %I Association des Annales de l'Institut Fourier %U https://www.numdam.org/articles/10.5802/aif.1489/ %R 10.5802/aif.1489 %G en %F 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, Tome 45 (1995) no. 4, pp. 1135-1162. doi: 10.5802/aif.1489
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