Abstract.Suppose we have a complex analytic family, Vr \t\ < 1, such that the generic fibre is a nonsingular complex manifold of complex dimension n. Let T denote the monodromy induced from going once around the singular fibre and let / denote the identity map. We shall associate to the singular fibre a simplicial complex T, which is at most n-dimensional. Then under certain conditions on the family V, (which are satisfied for the Milnor fibration of an isolated singularity or if the V, are compact Kahler), there is an integer N > 0 such that (TN -¡fHk(V,) = 0 if and only if Hk(T) = 0.1. Introduction. 1.1. In this article, we let V be a complex hypersurface having normal crossings, where the complex dimension of V is «. Then we shall construct a simplicial complex T corresponding to V, where the real dimension of T is at most «. In fact, to each integer N > 0, we shall associate to F a complex TN, where Tx = T. Then we shall see how these complexes have applications in studying the monodromy about V.

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Abstract.Suppose we have a complex analytic family, Vr \t\ < 1, such that the generic fibre is a nonsingular complex manifold of complex dimension n. Let T denote the monodromy induced from going once around the singular fibre and let / denote the identity map. We shall associate to the singular fibre a simplicial complex T, which is at most n-dimensional. Then under certain conditions on the family V, (which are satisfied for the Milnor fibration of an isolated singularity or if the V, are compact Kahler), there is an integer N > 0 such that (TN -¡fHk(V,) = 0 if and only if Hk(T) = 0.1. Introduction. 1.1. In this article, we let V be a complex hypersurface having normal crossings, where the complex dimension of V is «. Then we shall construct a simplicial complex T corresponding to V, where the real dimension of T is at most «. In fact, to each integer N > 0, we shall associate to F a complex TN, where Tx = T. Then we shall see how these complexes have applications in studying the monodromy about V.

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