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. (English) Zbl 1394.57026
For a Morin map \(f:M\to N\), where \(M\) is a compact and \(N\) a connected manifold, N. Dutertre and 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.
Reviewer: Thomas J. Bartsch (Gießen)
MSC:
| 57R45 | Singularities of differentiable mappings in differential topology |
| 57R70 | Critical points and critical submanifolds in differential topology |
Citations:
Zbl 1294.57018References:
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