Links of Singularities of Inner Non-degenerate Mixed Functions

We introduce the notion of a (strongly) inner non-degenerate mixed function \(f:{\mathbb {C}}^2\rightarrow {\mathbb {C}}.\) $f:{\mathbb{C}}^2\to \mathbb{C}.$ We show that inner non-degenerate mixed polynomials have weakly isolated singularities and strongly inner non-degenerate mixed polynomials have isolated singularities. Furthermore, under one additional assumption, which we call “ \(\Gamma \) $\mathrm{\Gamma }$ -niceness”, the links of these singularities can be completely characterized in terms of the Newton boundary of f. In particular, adding terms above the Newton boundary does not affect the topology of the link.