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Proceedings of the American Mathematical Society

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

 

 

Note on the embedding of manifolds in Euclidean space


Authors: J. C. Becker and H. H. Glover
Journal: Proc. Amer. Math. Soc. 27 (1971), 405-410
MSC: Primary 57.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0268903-0
MathSciNet review: 0268903
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Abstract: M. Hirsch and independently H. Glover have shown that a closed $ k$-connected smooth $ n$-manifold $ M$ embeds in $ {R^{2n - j}}$ if $ {M_0}$ immerses in $ {R^{2n - j - 1}},j \leqq 2k$ and $ 2j \leqq n - 3$. Here $ {M_0}$ denotes $ M$ minus the interior of a smooth disk. In this note we prove the converse and show also that the isotopy classes of embeddings of $ M$ in $ {R^{2n - j}}$ are in one-one correspondence with the regular homotopy classes of immersions of $ {M_0}$ in $ {R^{2n - j - 1}},j \leqq 2k - 1$ and $ 2j \leqq n - 4$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0268903-0
Keywords: Tubular neighborhood, deleted product, equivariant map, obstruction theory, Postnikov resolution
Article copyright: © Copyright 1971 American Mathematical Society