On the normal bundle of a manifold.
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This article is published in Pacific Journal of Mathematics.The article was published on 1964-12-01 and is currently open access. It has received 16 citations till now. The article focuses on the topics: Connection (principal bundle) & Normal bundle.read more
Citations
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Nonorientable surfaces in homology cobordisms
TL;DR: In this article, the authors investigate constraints on embeddings of a nonorientable surface in a 4-manifold with the homology of M I, where M I is a rational homology 3-sphere.
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Pontryagin squares in the Thom space of a bundle.
TL;DR: In this article, the action of the Pontryagin squares in the cohomology of the Thorn space of a vector bundle is investigated. But the results of the normal bundle of a manifold imbedded in Euclidean space are not applicable to the case of an orientable manifold.
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Submanifolds and the Hofer norm
TL;DR: In this paper, it was shown that for the Chekanov-Hofer pseudometric on the orbit of a closed submanifold to be a genuine metric, it is necessary for the sub-manifolds to be coisotropic, and this condition is sufficient under various additional geometric assumptions.
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Non-orientable surfaces in homology cobordisms
TL;DR: In this article, the authors consider the problem of embedding a non-orientable surface in a 4-manifold with the homology of the genus and normal Euler class of the surface.
References
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Classification of oriented sphere bundles over a 4-complex
A. Dold,H. Whitney +1 more
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On the embeddability of the real projective spaces
TL;DR: Hartman and Nirenberg as discussed by the authors, on spherical image maps whose Jacobians do not change sign, Amer. Math. Soc. 79 (1957), 306-318.