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Duality in toric topology

Duality in toric topology
Duality in toric topology

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

1069-5265
137-147
Springer Cham
Grbić, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Staniforth, Matthew
e193bd43-08d7-4034-bd94-ef0227592ed1
Bahri, Anthony
Jeffrey, Lisa
Panov, Taras
Stanley, Donald
Theriault, Stephen
Grbić, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Staniforth, Matthew
e193bd43-08d7-4034-bd94-ef0227592ed1
Bahri, Anthony
Jeffrey, Lisa
Panov, Taras
Stanley, Donald
Theriault, Stephen

Grbić, Jelena and Staniforth, Matthew (2024) Duality in toric topology. In, Bahri, Anthony, Jeffrey, Lisa, Panov, Taras, Stanley, Donald and Theriault, Stephen (eds.) Toric Topology and Polyhedral Products. (Fields Institute Communications, 89) Springer Cham, pp. 137-147. (doi:10.1007/978-3-031-57204-3_8).

Record type: Book Section

Abstract

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

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Accepted/In Press date: 7 April 2022
e-pub ahead of print date: 29 February 2024
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Identifiers

Local EPrints ID: 493360
URI: http://eprints.soton.ac.uk/id/eprint/493360
DOI: doi:10.1007/978-3-031-57204-3_8
ISSN: 1069-5265
PURE UUID: 01deed18-216e-4020-99a5-8d23f353a1ae
ORCID for Jelena Grbić: ORCID iD orcid.org/0000-0002-7164-540X

Catalogue record

Date deposited: 30 Aug 2024 16:36
Last modified: 31 Aug 2024 01:46

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Contributors

Author: Jelena Grbić ORCID iD
Author: Matthew Staniforth
Editor: Anthony Bahri
Editor: Lisa Jeffrey
Editor: Taras Panov
Editor: Donald Stanley
Editor: Stephen Theriault

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