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Function germs defined on isolated hypersurface singularities. (English) Zbl 0548.32005
Let (X,0) be an isolated hypersurface singularity. In this paper we study analytic function germs (X,0)\(\to ({\mathbb{C}},0)\) under right and contact equivalence relations. We describe the classes of singularities (X,0) on which there are simple functions and give some classification lists of simple germs. - The case when (X,0) is an isolated singularity of a complete intersection was treated similarly in our paper in Math. Ann. 267, 461-472 (1984; Zbl 0519.32009) giving an extension of a theorem of J. N. Mather and S. S.-T. Yau [Invent. Math. 69, 243-251 (1982; Zbl 0499.32008)]. Moreover, it is possible to construct a monodromy exact sequence associated to a function germ \(f:(X,0)\to ({\mathbb{C}},0),\) which is a contact invariant of f, as it is shown in the author’s paper in Compos. Math. 54, 105-119 (1985).

MSC:
32B10 Germs of analytic sets, local parametrization
32S05 Local complex singularities
14J17 Singularities of surfaces or higher-dimensional varieties
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
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