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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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 $ {M^m} \to {Q^q}$ which in the appropriate local coordinate systems has the form $ {R^m} \to {R^q}$ 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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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