ar X iv : m at h / 05 12 49 7 v 4 [ m at h . A T ] 8 M ay 2 00 7 MOMENT - ANGLE COMPLEXES , MONOMIAL IDEALS , AND MASSEY PRODUCTS

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatorics of the underlying simplicial complex. Applications to the study of non-formal manifolds and subspace arrangements are given.