The Polyhedral Product Functor: a Method of Computation for Moment-angle Complexes, Arrangements and Related Spaces

This article gives a natural decomposition of the suspension of generalized moment-angle complexes or partial product spaces which arise as polyhedral product functors described below. In the special case of the complements of certain subspace arrangements, the geometrical decomposition implies the homological decomposition in Goresky-MacPherson [20], Hochster[22], Baskakov [3], Panov [36], and Buchstaber-Panov [7]. Since the splitting is geometric, an analogous homological decomposition for a generalized moment-angle complex applies for any homology theory. This decomposition gives an additive decomposition for the Stanley-Reisner ring of a finite simplicial complex and generalizations of certain homotopy theoretic results of Porter [39] and Ganea [19]. The spirit of the work here follows that of Denham-Suciu in [16].