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Transactions of the American Mathematical Society
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
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\geq2$) 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

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04326-1
PII: S 0002-9947(06)04326-1
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.