A spectral sequence for polyhedral products
Algebraic Topology
2015-11-30 v1 Combinatorics
K-Theory and Homology
Abstract
The purpose of this paper is to exhibit fine structure for polyhedral products Z(K;(X,A) and polyhedral smash products . (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.
Keywords
Cite
@article{arxiv.1511.08292,
title = {A spectral sequence for polyhedral products},
author = {A. Bahri and M. Bendersky and F. R. Cohen and S. Gitler},
journal= {arXiv preprint arXiv:1511.08292},
year = {2015}
}