Homology of iterated semidirect products of free groups
- Author(s): Cohen, Daniel C.
- Suciu, Alexander I.
- et al.
Published Web Locationhttps://arxiv.org/pdf/alg-geom/9503002.pdf
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. Our construction also yields algorithms for computing the homology of the Milnor fiber of a fiber-type hyperplane arrangement, and more generally, the homology of the complement of such an arrangement with coefficients in an arbitrary local system.