An alternative proof of a formula on Euler characteristics of singularity sets of a Morin map \(M \rightarrow \mathbb{R}^n\) based on Morse theory
For a Morin map \(f:M\to N\), where \(M\) is a compact and \(N\) a connected manifold, \textit{N. Dutertre} and \textit{T. Fukui} established a formula (Theorem 6.2 of [J. Math. Soc. Japan 66, No. 1, 161--203 (2014; Zbl 1294.57018)]) relating the Euler characteristic of \(M\) and the Euler characteristic of the singular sets of \(f\). The present paper gives a new proof of this result in the special case \(N=\mathbb{R}^n\) using Morse theory on manifolds with boundary.
scientific article; zbMATH DE number 6822544
scientific article