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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Handle attaching on generic maps
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by Youn W. Lee PDF
Trans. Amer. Math. Soc. 279 (1983), 77-94 Request permission

Abstract:

Using the handle attaching technique along the singular value set of generic maps in the stable range together with the handle subtraction of Haefliger, smooth immersions and embeddings are studied. We generalize Whitney’s immersion theorem, and Haefliger and Hirsh’s result on embedding and classification of embeddings of $k$-connected ($(k + 1)$-connected for the classification) smooth $n$-manifolds into ${{\mathbf {R}}^{2n - k}}$. For example, we obtain the following as a generalization of Whitney’s immersion theorem. If $f: {V^n} \to {M^m}, {3n} < {2m}$, is a generic map such that each component of its double point set is either a closed manifold or diffeomorphic to the $(2n - m)$-disk, then $f$ is homotopic to an immersion.
References
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 279 (1983), 77-94
  • MSC: Primary 57R40; Secondary 57R42, 57R65
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0704603-0
  • MathSciNet review: 704603