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Proceedings of the American Mathematical Society

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

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Induction on symmetric axial maps and embeddings of projective spaces
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by A. J. Berrick PDF
Proc. Amer. Math. Soc. 60 (1976), 276-278 Request permission

Abstract:

A homotopy class of axial maps ${P^n} \times {P^n} \to {P^{n + k}}$ determines an invariant in ${\pi _n}({V_{n + k + 1,n + 1}})\;(2k \geqslant n + 2)$. If an axial map is symmetric and has trivial invariant it extends to a symmetric axial map ${P^{n + 1}} \times {P^{n + 1}} \to {P^{n + k + 1}}$. An immersion of ${P^n}$ in ${R^{n + k}}$ lifts to an immersion of ${S^n}$ in ${R^{n + k}}$ and so has a Smale invariant. For $j:{R^{n + k}}\hookrightarrow {R^{n + k + 2}},2k \geqslant n + 2$ (resp. $2k \geqslant n + 3$), any embedding $a:{P^n} \to {R^{n + k}}$ with trivial Smale invariant induces an embedding of ${P^{n + 1}}$ in ${R^{n + k + 2}}$ whose restriction to ${P^n}$ is regularly homotopic (resp. isotopic) to ja.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 276-278
  • MSC: Primary 57D40
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0420661-7
  • MathSciNet review: 0420661