Duality in Toric Topology

Jelena Grbić; Matthew Staniforth

Duality in Toric Topology

Algebraic Topology 2022-02-01 v2

Authors: Jelena Grbić , Matthew Staniforth

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.

Keywords

toric varieties algebraic tori

Cite

@article{arxiv.2107.05974,
  title  = {Duality in Toric Topology},
  author = {Jelena Grbić and Matthew Staniforth},
  journal= {arXiv preprint arXiv:2107.05974},
  year   = {2022}
}

Comments

10 pages

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