We use stratified Morse theory to construct a complex to compute the cohomology of the complement of a hyperplane arrangement with coefficients in a complex rank one local system. The linearization… (More)

A b st r ac t . The Chen groups of a group are the lower central series quotients of its maximal metabelian quotient. We show that the Chen groups of the pure braid group Pn are free abelian, and we… (More)

A b st r ac t . To a plane algebraic curve of degree n, Moishezon associated a braid monodromy homomorphism from a finitely generated free group to Artin’s braid group Bn. Using Hansen’s polynomial… (More)

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… (More)

Let A be an arrangement of n complex hyperplanes. The fundamental group of the complement of A is determined by a braid monodromy homomorphism, α : Fs → Pn. Using the Gassner representation of the… (More)

We prove a vanishing theorem for the cohomology of the complement of a complex hyperplane arrangement with coefficients in a complex local system. This result is compared with other vanishing… (More)

Motivated by the Milnor fiber of a central arrangement, we study the cohomology of a family of cyclic covers of the complement of an arbitrary arrangement. We give an explicit proof of the polynomial… (More)

We study the topology of the boundary manifold of a line arrangement in CP , with emphasis on the fundamental group G and associated invariants. We determine the Alexander polynomial .G/ , and more… (More)