Parallel connections and bundles of arrangements (Q5960428)

Let \(\mathcal A\) be a linear complex hyperplane arrangement. It is here shown that the projection along any modular flat \(X\) induces a locally trivial fibration of the complement, with trivial monodromy action. Whence the Leray-Serre spectral sequence degenerates at \(E_2\), which may be used to explain the factorization of the Poincaré polynomial of the complement. Thus the paper sharpens and completes the earlier analysis of the topological effects of a modular flat by Stanley, Brylawski, Terao, Jambu, and Paris. NEWLINENEWLINENEWLINEMoreover, the special case of an arrangement that realizes a ``generalized parallel connection of matroids'' is studied. In this case the fibration associated with the connecting modular flat is trivial. Finally, examples of \(K(\pi, 1)\)-arrangements as well as of non-\(K(\pi, 1)\)-arrangements are derived.