Moment-angle complexes, monomial ideals and Massey products

Abstract

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.