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Transactions of the American Mathematical Society

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

 
 

 

A homotopy principle for maps with prescribed Thom-Boardman singularities


Author: Yoshifumi Ando
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
Published electronically: September 19, 2006
MathSciNet review: 2255183
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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

Keywords: Homotopy principle, Thom-Boardman singularity, jet space, Boardman manifold
Received by editor(s): September 15, 2003
Published electronically: September 19, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.