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On immersions of N-manifolds in codimension N − 1

Part of: Differential topology

Published online by Cambridge University Press:  09 April 2009

M. A. Aguilar  and
G. Pastor
M. A. Aguilar
Affiliation:
Instituto de Matemáticas, Universidad Nacional, Autónoma de México, Ciudad Universitaria, 04510 México, D.F., Mexico
G. Pastor
Affiliation:
Departamento de Matem´ticas, Centro de Investigación y, Estudios Avanzados del I.P.N., Apartado Postal 14-740, 07000 México, D.F., Mexico
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Abstract

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We give a simple proof, using only classical algebraic topology, of the following theorem of B. H. Li and F. P. Peterson. Any map from an N-manifold into a (2N − 1)-manifold is homotopic to an immersion.

MSC classification

Secondary: 57R42: Immersions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 2 , October 1988 , pp. 184 - 186
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Dyer, E., Cohomology theories, W. A. Benjamin, New York, 1969.Google Scholar
[2]Hirsch, M. W., ‘Immersions of manifolds’, Trans. Amer. Math. Soc. 93 (1959), 242–276.CrossRefGoogle Scholar
[3]Holm, P., ‘Microbundles and S-duality’, Acta Math. 118 (1968), 271–296.CrossRefGoogle Scholar
[4]Li, B. H. and Peterson, F. P., ‘On immersions of k-manifolds in (2k − 1)-manifolds’, Proc. Amer. Math. Soc. 83 (1981), 159–162.Google Scholar
[5]Steenrod, N., The topology of fiber bundles, Princeton University Press, Princeton, N. J., 1951.CrossRefGoogle Scholar
[6]Whitney, H., ‘Differentiable manifolds’, Ann. of Math. 37 (1936), 645–680.CrossRefGoogle Scholar