2007/11/29 by Abbas Bahri, Bahri, A., Martin Bendersky +5 · 14 citations
Mathematics · #13F55 #14F45 #32S22 #52C35 (Primary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0711.4689
openalex publication_date 2007/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citegoresky.macpherson, Hochster\citehochster, Baskakov \citebaskakov, Panov \citepanov, and Buchstaber-Panov \citebuchstaber.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 \citeporter and Ganea \citeganea. The spirit of the work here follows that of Denham-Suciu in \citedenham.suciu.