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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