Abstract
The purpose of this paper is to exhibit fine structure for polyhedral products Z(K;(X_,A_)) and polyhedral smash products Zˆ(K;(X_,A_)) where moment-angle complexes are special cases in which (X,A)=(D2,S1). There are three main parts to this paper.(1)One part gives a natural filtration of the polyhedral product together with properties of the resulting spectral sequence in Theorem 2.15. Applications of this spectral sequence are given.(2)The second part gives a homological decomposition of Zˆ(K;(X_,A_)) in case (X_,A_) consists of CW pairs by using part 1.(3)Applications to the ring structure of Z(K;(X_,A_)) are given for CW-pairs (X,A) satisfying suitable freeness conditions.
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