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One-relator groups and algebras related to polyhedral products

One-relator groups and algebras related to polyhedral products
One-relator groups and algebras related to polyhedral products

We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex K, we specify a necessary and sufficient combinatorial condition for the commutator subgroup RC'Kof a right-angled Coxeter group, viewed as the fundamental group of the real moment-angle complex RK, to be a one-relator group; and for the Pontryagin algebra H(ΩZK) of the moment-angle complex to be a one-relator algebra. We also give a homological characterization of these properties. For RC'K, it is given by a condition on the homology group H2(RK), whereas for H(ΩZK) it is stated in terms of the bigrading of the homology groups of ZK

Commutator subgroups of right-angled Coxeter groups, Flag complexes, Moment-angle complexes, One-relator groups and algebras
0308-2105
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Simmons, George
ea6e69af-3214-49e6-b7e1-66eda67bc42c
Ilyasova, Marina
41f2fc44-45dd-41ff-8fa9-677fb02fadfd
Panov, Taras
78d6f427-3f3d-481c-98be-6869370101aa
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Simmons, George
ea6e69af-3214-49e6-b7e1-66eda67bc42c
Ilyasova, Marina
41f2fc44-45dd-41ff-8fa9-677fb02fadfd
Panov, Taras
78d6f427-3f3d-481c-98be-6869370101aa

Grbic, Jelena, Simmons, George, Ilyasova, Marina and Panov, Taras (2021) One-relator groups and algebras related to polyhedral products. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. (doi:10.1017/prm.2020.101).

Record type: Article

Abstract

We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex K, we specify a necessary and sufficient combinatorial condition for the commutator subgroup RC'Kof a right-angled Coxeter group, viewed as the fundamental group of the real moment-angle complex RK, to be a one-relator group; and for the Pontryagin algebra H(ΩZK) of the moment-angle complex to be a one-relator algebra. We also give a homological characterization of these properties. For RC'K, it is given by a condition on the homology group H2(RK), whereas for H(ΩZK) it is stated in terms of the bigrading of the homology groups of ZK

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One-relator groups and algebras related to polyhedral products - Accepted Manuscript
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Accepted/In Press date: 14 January 2021
e-pub ahead of print date: 15 January 2021
Published date: 15 January 2021
Additional Information: Publisher Copyright: © 2021 American Medical Association. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
Keywords: Commutator subgroups of right-angled Coxeter groups, Flag complexes, Moment-angle complexes, One-relator groups and algebras

Identifiers

Local EPrints ID: 447424
URI: http://eprints.soton.ac.uk/id/eprint/447424
ISSN: 0308-2105
PURE UUID: 0ced18bb-1f27-4445-8078-797e950a7bcd
ORCID for Jelena Grbic: ORCID iD orcid.org/0000-0002-7164-540X

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Date deposited: 11 Mar 2021 17:32
Last modified: 17 Mar 2024 06:20

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Contributors

Author: Jelena Grbic ORCID iD
Author: George Simmons
Author: Marina Ilyasova
Author: Taras Panov

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