4 problems

Let $f,g\colon(\mathbb{C}^n,0)\to(\mathbb{C},0)$ be reduced holomorphic function-germs. Suppose there is a homeomorphism $\varphi\colon(\mathbb{C}^n,0)\to(\mathbb{C}^n,0)$ such tha…

Let $f,g\colon(\mathbb{C}^n,0)\to(\mathbb{C},0)$ be reduced holomorphic function-germs, and let $V(f)$ and $V(g)$ denote their zero-set germs at the origin. Suppose there is a home…

Topological classification conjecture. The two foliation germs are topologically equivalent if and only if: (1) the ray configurations of their eigenvalue tuples are equivalent; an…

Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be foliations by curves on $(\mathbb{C}^3,0)$. Suppose they are topologically equivalent and do not admit invariant surfaces over which the…