Duality in Toric Topology
Jelena Grbi\'c, Matthew Staniforth
TL;DR
This paper characterizes Poincaré duality in moment-angle complexes using combinatorial and algebraic dualities, extending results to polyhedral products and their algebraic structures.
Contribution
It provides a combinatorial and algebraic characterization of Poincaré duality in moment-angle complexes and extends duality results to polyhedral join products.
Findings
Characterization of integral Poincaré duality moment-angle complexes
Connection between Fan-Wang duality and Gorenstein duality
Extension of duality results to polyhedral join products
Abstract
We characterise integral Poincar\'e duality moment-angle complexes in combinatorial terms of the Fan-Wang duality of the simplicial complex , and consequently in algebraic terms of the Gorenstein duality of the Stanley-Reisner ring . We extend Poincar\'e duality results to certain polyhedral products using polyhedral join products of simplicial complexes.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology