Some Open Problems in Complex Singularities

Abstract

We discuss some open problems and questions related with five different topics in complex singularities. These are: (i) Topological and holomorphic ranks of an isolated singularity germ and the Zariski-Lipman conjecture; (ii) Graph manifolds and links of surface singularities. (iii) Milnor’s fibration for complex singularities and the topology of analytic foliations near an isolated singularity. (iv) Rochlin’s signature theorem and Gorenstein surface singularities. (v) The index of a vector field on a singular variety. These are all topics on which I have been interested for a long time.