On Polyhedral Product Spaces over Polyhedral Joins
Abstract
The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitler's J-construction and simplicial wedge construction. This article gives a cohomological decomposition of a polyhedral product over a polyhedral join for certain families of pairs of simplicial complexes. A formula for the Hilbert-Poincar\'e series is given, which generalizes Ayzenberg's formula for the moment-angle complex.
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