HOMOLOGY OF ITERATED SEMIDIRECT PRODUCTS OF FREE GROUPS

Let G be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of G. This resolution is used to define representations of groups which act compatibly on G, generalizing classical constructions of Magnus, Burau, and Gassner. O ur construction also yields algorithms for computing the homology of t he Milnor fiber of a fiber-type hyperplane arrangement, and more gener ally, the homology of the complement of such an arrangement with coeff icients in an arbitrary local system. (C) 1998 Elsevier Science B.V.