COHOMOLOGY OF THE COMPLEMENT OF A FREE DIVISOR

We prove that if D is a ''strongly quasihomogeneous'' free divisor in the Stein manifold X, and U is its complement, then the de Rham cohomo logy of U can be computed as the cohomology of the complex of meromorp hic differential forms on X with logarithmic poles along D, with exter ior derivative. The class of strongly quasihomogeneous free divisors, introduced here, includes free hyperplane arrangements and the discrim inants of stable mappings in Mather's nice dimensions (and in particul ar the discriminants of Coxeter groups).