The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces

This article gives a natural decomposition of the suspension of generalized moment-angle complexes or partial product spaces which arise as polyhedral product functors described below. The geometrical decomposition presented here provides structure for the stable homotopy type of these spaces includ...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2010-10, Vol.225 (3), p.1634-1668
Main Authors: Bahri, A., Bendersky, M., Cohen, F.R., Gitler, S.
Format: Article
Language:English
Subjects:
Arrangements
Cohomology ring
Moment-angle complex
Simplicial complex
Simplicial sets
Stable splittings
Stanley–Reisner ring
Suspensions
Toric varieties
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Summary:This article gives a natural decomposition of the suspension of generalized moment-angle complexes or partial product spaces which arise as polyhedral product functors described below. The geometrical decomposition presented here provides structure for the stable homotopy type of these spaces including spaces appearing in work of Goresky–MacPherson concerning complements of certain subspace arrangements, as well as Davis–Januszkiewicz and Buchstaber–Panov concerning moment-angle complexes. Since the stable decompositions here are geometric, they provide corresponding homological decompositions for generalized moment-angle complexes for any homology theory.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2010.03.026