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We give a formula for the Euler characteristic of the Milnor bre of any analytic function f of two variables. This formula depends on the intersection multiplicities, the Milnor numbers and the powers of the branches of the germ of the curve dened by f: The goal of the formula is that it use neither the resolution nor the deformations of f: Moreover, it can be use for giving an algorithm to compute it.

Euler characteristic of the Milnor fibre of plane singularities