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Topological types of complex isolated hypersurface singularities. (English) Zbl 0674.32006

There are four different definitions of topological types of a holomorphic germ which has an isolated critical point at the origin. They are called that “topologically right equivalent”, “topologically right-left equivalent”, “topologically V-equivalent” and “link equivalent”.
In this paper, the author considers and studies whether those definitions are equivalent or not. By the definitions, the right equivalence implies the right-left equivalence, which in turn implies the V-equivalence. And the link equivalence obviously implies the V-equivalence.
Theorem 1. If two holomorphic function germs with isolated critical points at the origin are topologically V-equivalent, then they are link equivalent.
Theorem 2. Let f and g be holomorphic function germs with isolated critical points at the origin. Then the following three are equivalent. (a) f and g are topologically right-left equivalent. (b) f and g are topologically V-equivalent. (c) f and g are link equivalent.
Reviewer: S.Ohyanagi

MSC:

32Sxx Complex singularities
32S05 Local complex singularities
14J17 Singularities of surfaces or higher-dimensional varieties
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