Euler characteristic of the Milnor fibre of plane singularities

Abstract

We give a formula for the Euler characteristic of the Milnor fibre of any analytic function f of two variables. This formula depends on the intersection multiplicity, the multiplicity and the Milnor number of the branches of the germ of curve defined by f. The goal of the formula is that it uses neither the resolution nor the deformations of f. Moreover, it can be used for giving an algorithm to compute it.