On the topology and combinatorics of decomposable arrangements

We study topological properties of complex hyperplane arrangements that are decomposable. When this purely combinatorial condition is satisfied, it is known that the associated graded Lie algebra of the arrangement group G G decomposes (in degrees greater than 1 1 ) as a direct product of free Lie algebras. It follows that the I I -adic completion of the Alexander invariant B ( G ) B(G) also decomposes as a direct sum of “local” invariants and the Chen ranks of G G are the sums of the local contributions. Moreover, if B ( G ) B(G) is separated, then the degree 1 1 cohomology jump loci of the arrangement complement have only local components, and the algebraic monodromy of the Milnor fibration is trivial in degree 1 1 .