The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces
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Publication:2637924
DOI10.1016/J.AIM.2010.03.026zbMATH Open1197.13021arXiv0711.4689OpenAlexW2962858127WikidataQ56506171 ScholiaQ56506171MaRDI QIDQ2637924
Author name not available (Why is that?)
Publication date: 13 September 2010
Published in: (Search for Journal in Brave)
Abstract: This article gives a natural decomposition of the suspension of generalized moment-angle complexes or {it partial product spaces} which arise as {it polyhedral product functors} described below. In the special case of the complements of certain subspace arrangements, the geometrical decomposition implies the homological decomposition in Goresky-MacPherson cite{goresky.macpherson}, Hochstercite{hochster}, Baskakov cite{baskakov}, Panov cite{panov}, and Buchstaber-Panov cite{buchstaber.panov}. Since the splitting is geometric, an analogous homological decomposition for a generalized moment-angle complex applies for any homology theory. This decomposition gives an additive decomposition for the Stanley-Reisner ring of a finite simplicial complex and generalizations of certain homotopy theoretic results of Porter cite{porter} and Ganea cite{ganea}. The spirit of the work here follows that of Denham-Suciu in cite{denham.suciu}.
Full work available at URL: https://arxiv.org/abs/0711.4689
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