In this paper we extend Y. Eliashberg’s theorem on the maps with fold type singularities to arbitrary Thom-Boardman singularities. Namely, we state a necessary and sufficient condition for a continuous map of smooth manifolds of the same dimension to be homotopic to a generic map with a prescribed Thom-Boardman singularity ΣI at each point. In dimensions 2 and 3 we rephrase this condition in terms of the homology classes of the given singular loci and the characteristic classes of the manifolds.

中文翻译：

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具有指定博德曼奇点的地图

在本文中，我们将 Y. Eliashberg 定理在具有折叠类型奇点的映射上扩展到任意 Thom-Boardman 奇点。即，我们陈述了相同维度的光滑流形的连续映射与在每个点具有规定的 Thom-Boardman 奇点 ΣI 的通用映射同伦的充分必要条件。在维度 2 和 3 中，我们根据给定奇异位点的同源类和流形的特征类来重新表述这个条件。