Remarks on Laufer’s formula for the Milnor number, Rochlin’s signature theorem and the analytic Euler characteristic of compact complex manifolds

Introduction. There are several classical approaches to studying the geometry and topology of isolated singularities (V, 0) defined by a holomorphic map-germ (C, 0) f → (C, 0). One of these is by looking at resolutions of the singularity, π : Ṽ → V . Another is by considering the non-critical levels of the function f and the way how these degenerate to the special fiber V . Laufer’s formula for the Milnor number establishes a beautiful bridge between these two points of view. The formula says that if n = 3, then one has: