## 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

### Citations:

Zbl 0548.32004; Zbl 0531.32006; Zbl 0519.32009; Zbl 0499.32008
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### References:

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