Topological types of complex isolated hypersurface singularities
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.
scientific article; zbMATH DE number 4103448