Mersions of topological manifolds

Author:
David Gauld

Journal:
Trans. Amer. Math. Soc. **149** (1970), 539-560

MSC:
Primary 57.01

MathSciNet review:
0266217

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Abstract: We here generalise the immersion and submersion theorems of Smale, Hirsch, Haefliger and Poenaru, Phillips, Lees, and Lashof, giving a relative version in the case of mersions of topological manifolds. A mersion is a map of manifolds which in the appropriate local coordinate systems has the form of the standard inclusion or projection of one euclidean space in another. Such a mersion induces a map of tangent bundles satisfying certain properties. In this paper the problem of classifying mersions is reduced to that of classifying such bundle maps.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1970-0266217-X

Keywords:
Classification of immersions,
classification of submersions,
tangent bundles,
differential of an immersion,
differential of a submersion,
realisation of regular homotopy by isotopy

Article copyright:
© Copyright 1970
American Mathematical Society