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Conjugaison topologique des germes de fonctions holomorphes à singularité isolée en dimension trois. (French) Zbl 0575.32005

The main result of this paper is the following.
Theorem. Let \(f_ 0, f_ 1: ({\mathbb{C}}^ n,0)\to ({\mathbb{C}},0)\) be two germs of analytic functions with isolated singularities at the origin. Then \(f_ 0\) is R-L-equivalent to \(f_ 1\) (resp. R-equivalent) if and only if \(f_ 0^{-1}(0)\) and \(f_ 1^{-1}(0)\) have the same topological type (resp. strongly same topological type) at 0.
This theorem is proved by King for \(n\neq 3\) and by the author for \(n=3\).
Reviewer: M.Oka

MSC:

32B10 Germs of analytic sets, local parametrization
32S05 Local complex singularities
55P10 Homotopy equivalences in algebraic topology
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References:

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