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The Euler characteristic of the disentanglement of the image of a corank 1 map germ. (English) Zbl 0734.58013
Singularity theory and its applications. Pt. I: Geometric aspects of singularities, Proc. Symp., Warwick/UK 1988-89, Lect. Notes Math. 1462, 212-220 (1991).
[For the entire collection see Zbl 0723.00028.]
A finitely \({\mathcal A}\)-determined map germ \(f_ 0: ({\mathbb{C}}^ n,0)\to ({\mathbb{C}}^ p,0)\), \(2\leq n<p\) is considered. It is assumed that (n,p) is in the range of nice dimensions. The main result expresses the Euler characteristic of the image of a stabilization of \(f_ 0\) in terms of the Milnor number of the multiple point schemes of \(f_ 0\), in the case where \(f_ 0\) is of corank 1.

MSC:
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants
58A35 Stratified sets