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 $\hat{Z}(K;(X,A)$. (Moment-angle complexes are special cases for which (X,A) = (D^2,S^1)). 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.

References in corpus (6)

• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces
• Cup-products in generalized moment-angle complexes
• The homology coalgebra and cohomology algebra of generalized moment-angle complexes
• On products in a real moment-angle manifold
• The homotopy type of the polyhedral product for shifted complexes
• The Euler characteristic of a polyhedral product

Cited by in corpus (1)

• Bredon Cohomology of Polyhedral Products