On Polyhedral Product Spaces over Polyhedral Joins

摘要

The construction of a simplicial complex given by polyhedral joins(introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen andGitler's $J$-construction and simplicial wedge construction. This article givesa cohomological decomposition of a polyhedral product over a polyhedral joinfor certain families of pairs of simplicial complexes. A formula for theHilbert-Poincar\'{e} series is given, which generalizes Ayzenberg's formula forthe moment-angle complex.