Dutertre和Fukui关于Morin奇点的一个定理的新证明
A new proof of a theorem of Dutertre and Fukui on Morin singularities
摘要：
在[2]中，N.Dutertre和T.福井用维罗的积分学拓扑结构的稳定映射$f:M\rightarrow N$之间的两个光滑流形$M$和$N$。他们还讨论了Morin映射的几个应用。特别地，在定理6.2 [2]中，他们给出了紧致流形$M$的欧拉示性数线与定义在$M$上的Morin映射的奇异集的欧拉示性数线之间的关系。本文将莫尔斯理论应用于Morin映射的奇异集的研究，给出了当$N=\mathbb{R}^n$ .
英文摘要：
In [2], N.Dutertre and T. Fukui used Viro's integral calculus to study the topology of stable maps $f:M\rightarrow N$ between two smooth manifolds $M$ and $N$. They also discussed several applications to Morin maps. In particular, in Theorem 6.2 [2], they show an equality relating the Euler characteristic of a compact manifold $M$ and the Euler characteristic of the singular sets of a Morin map defined on $M$. In this paper we show how Morse theory for manifolds with boundary can be applied to the study of the singular sets of a Morin map in order to obtain a new proof of Dutertre-Fukui's Theorem when $N=\mathbb{R}^n$.
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