A criterion for topological equivalence of two variable complex analytic function germs

Abstract

We show that two analytic function germs $(\mathbf{C}^{2},0) \to (\mathbf{C},0)$ are topologically right equivalent if and only if there is a one-to-one correspondence between the irreducible components of their zero sets that preserves the multiplicites of these components, their Puiseux pairs, and the intersection numbers of any pair of distinct components.