Duality in Toric Topology

We characterise integral Poincaré duality moment-angle complexes \(\mathcal {Z}_{\mathcal {K}}\) in combinatorial terms of the Alexander duality of the simplicial complex \(\mathcal {K}\) and consequently in algebraic terms of the Gorenstein duality of the Stanley-Reisner ring \(\mathbb {Z}[\mathcal {K}]\) . We extend Poincaré duality results to certain polyhedral products using polyhedral join products of simplicial complexes.