CONSTRUCTING GENERIC SMOOTH MAPS OF A MANIFOLD INTO A SURFACE WITH PRESCRIBED SINGULAR LOCI

Authors
SAEKI O
Citation
O. Saeki, CONSTRUCTING GENERIC SMOOTH MAPS OF A MANIFOLD INTO A SURFACE WITH PRESCRIBED SINGULAR LOCI, Annales de l'Institut Fourier, 45(4), 1995, pp. 1135
Citations number
15
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Annales de l'Institut Fourier → ACNP
ISSN journal
03730956
Volume
45
Issue
4
Year of publication
1995
Database
ISI
SICI code
0373-0956(1995)45:4<1135:CGSMOA>2.0.ZU;2-I
Abstract
It is known that the singular set S(f) of a generic smooth map f : M - -> N of an n-dimensional manifold into a surface is a closed 1-dimensi onal submanifold of M and that it has a natural stratification induced by the absolute index. In this paper, we give a complete characteriza tion of those 1-dimensional (stratified) submanifolds which arise as t he singular set of a generic map in terms of the homology class they r epresent.