A Homotopy Principle for Maps with Prescribed Thom-boardman Singularities
نویسنده
چکیده
Let N and P be smooth manifolds of dimensions n and p (n ≥ p ≥ 2) respectively. Let Ω (N, P ) denote an open subspace of J∞(N, P ) which consists of all Boardman submanifolds Σ (N, P ) of symbols J with J ≤ I. An Ω -regular map f : N → P refers to a smooth map having only singularities in Ω (N, P ) and satisfying transversality condition. We will prove what is called the homotopy principle for Ω -regular maps in the existence level. Namely, a continuous section s of Ω(N, P ) over N has an Ω -regular map f such that s and j∞f are homotopic as sections.
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