Moment-angle complexes, monomial ideals, and Massey products

Details Moment-angle complexes, monomial ideals, and Massey products Moment-angle complexes, monomial ideals, and Massey products

2005-12-21

arxiv.org/abs/math/0512497v4

Pure and Applied Mathematics Quarterly, 3(1) 2007, (Robert MacPherson special issue, part 3), 25--60

Mathematics

Algebraic Topology

30 pages. Published version

Scientific paper

Associated to every finite simplicial complex K there is a "moment-angle" finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K 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.

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