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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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A homotopy principle for maps with prescribed Thom-Boardman singularities
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by Yoshifumi Ando PDF
Trans. Amer. Math. Soc. 359 (2007), 489-515 Request permission

Abstract:

Let $N$ and $P$ be smooth manifolds of dimensions $n$ and $p$ ($n\geq p\geq 2$) respectively. Let $\Omega ^{I}(N,P)$ denote an open subspace of $J^{\infty }(N,P)$ which consists of all Boardman submanifolds $\Sigma ^{J}(N,P)$ of symbols $J$ with $J\leq I$. An $\Omega ^{I}$-regular map $f:N\rightarrow P$ refers to a smooth map such that $j^{\infty }f(N)\subset \Omega ^{I}(N,P)$. We will prove what is called the homotopy principle for $\Omega ^{I}$-regular maps on the existence level. Namely, a continuous section $s$ of $\Omega ^{I}(N,P)$ over $N$ has an $\Omega ^{I}$-regular map $f$ such that $s$ and $j^{\infty }f$ are homotopic as sections.
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Additional Information
  • Yoshifumi Ando
  • Affiliation: Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yamaguchi 753-8512, Japan
  • Email: andoy@yamaguchi-u.ac.jp
  • Received by editor(s): September 15, 2003
  • Published electronically: September 19, 2006
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 489-515
  • MSC (2000): Primary 58K30; Secondary 57R45, 58A20
  • DOI: https://doi.org/10.1090/S0002-9947-06-04326-1
  • MathSciNet review: 2255183