Signatures of Lefschetz fibrations

Let M be a smooth 4-manifold which admits a Lefschetz fibration over D2 or S2. We develop an algorithm to compute the signature of M using the global monodromy of this fibra-tion. As a corollary we prove that there is no hyperelliptic Lefschetz fibration over S2 with only reducible singular fibers. 0. Introduction. The signature of a smooth 4-manifold which admits a hyperelliptic Lefschetz fibration of genus g over a closed surface can be computed using the local signature formula given by Matsumoto ([M1], [M2]) for g = 1, 2 and more recently extended by Endo [E] for g ≥ 3