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arXiv · 1511.08292

A spectral sequence for polyhedral products

A. Bahri·M. Bendersky·F. R. Cohen·S. Gitler
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Abstract

The purpose of this paper is to exhibit fine structure for polyhedral products Z(K;(X,A) and polyhedral smash products $\widehat{Z}(K;(X,A)$. (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.

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BibTeXRIS

A. Bahri, M. Bendersky, F. R. Cohen, S. Gitler. 2015-11-26. A spectral sequence for polyhedral products. https://arxiv.org/abs/1511.08292

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