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-Poincaré series is given, which generalizes Ayzenberg's formula for the moment-angle complex.

Cited by in corpus (1)

• Loop spaces of polyhedral products associated with the polyhedral join product