A spectral sequence for polyhedral products
Abstract
The purpose of this paper is to exhibit fine structure for polyhedral products Z(K;(X,A) and polyhedral smash products Z(K;(X,A). (Moment-angle complexes are special cases for which (X,A) = (D2,S1)). There are three main parts. The first defines a natural filtration of the polyhedral product and derives properties of the resulting spectral sequence. This is followed with applications. The second part uses the first to give a homological decomposition of the polyhedral smash product. Finally there are applications to the ring structure of H*(Z(K;(X,A))) for CW-pairs (X,A) satisfying suitable freeness conditions.
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