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A homotopy principle for maps with prescribed Thom-Boardman singularities

Authors:	Yoshifumi Ando

Institution:	Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yamaguchi 753-8512, Japan

Abstract:	Let and be smooth manifolds of dimensions and ( $n\geq p\geq2$ ) 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 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 of $\Omega^{I}(N,P)$ over has an $\Omega^{I}$ -regular map such that and $j^{\infty}f$ are homotopic as sections.

Keywords:	Homotopy principle Thom-Boardman singularity jet space Boardman manifold

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