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Duality in Toric Topology (2107.05974v2)
Published 13 Jul 2021 in math.AT
Abstract: We characterise integral Poincar\'e duality moment-angle complexes $\mathcal{Z}_{\mathcal{K}}$ in combinatorial terms of the Fan-Wang 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 Poincar\'e duality results to certain polyhedral products using polyhedral join products of simplicial complexes.