Desingularizing maps of corank one
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- by S. J. Blank and C. Curley PDF
- Proc. Amer. Math. Soc. 80 (1980), 483-486 Request permission
Abstract:
In 1960, A. Haefliger presented necessary and sufficient conditions for factoring a smooth map from a surface into the plane through an immersion into ${R^3}$. Here, necessary and sufficient conditions are given for factoring a map between manifolds of dimension n, $n \geqslant 2$, through an immersion into a line bundle over the range. In addition, conditions are given for factoring such a map through a submersion from a line bundle over the domain.References
- André Haefliger, Quelques remarques sur les applications différentiables d’une surface dans le plan, Ann. Inst. Fourier (Grenoble) 10 (1960), 47–60 (French). MR 116357
- M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Graduate Texts in Mathematics, Vol. 14, Springer-Verlag, New York-Heidelberg, 1973. MR 0341518
- Yoshihiro Saito, On decomposable mappings of manifolds, J. Math. Kyoto Univ. 1 (1961/62), 425–455. MR 141134, DOI 10.1215/kjm/1250525014
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 483-486
- MSC: Primary 57R45; Secondary 58C27
- DOI: https://doi.org/10.1090/S0002-9939-1980-0581010-8
- MathSciNet review: 581010