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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Desingularizing maps of corank one


Authors: S. J. Blank and C. Curley
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
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] A. Haefliger, Quelques remarques sur les applications différentiables d'une surface dans le plan, Ann. Inst. Fourier (Grenoble) 10 (1960), 47-60. MR 0116357 (22:7145)
  • [2] M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Springer-Verlag, New York, 1973. MR 0341518 (49:6269)
  • [3] Y. Saito, On decomposable mappings of manifolds, J. Math. Kyoto Univ. 1 (1961/62), 425-455. MR 0141134 (25:4545)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0581010-8
Keywords: Immersion, submersion, line bundle, 2-generic, corank, Stiefel-Whitney class
Article copyright: © Copyright 1980 American Mathematical Society

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