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LS-category of moment-angle manifolds and higher order Massey products

LS-category of moment-angle manifolds and higher order Massey products
LS-category of moment-angle manifolds and higher order Massey products

Using the combinatorics of the underlying simplicial complex K, we give various upper and lower bounds for the Lusternik-Schnirelmann (LS) category of moment-angle complexes K{\mathcal{Z} {K}}. We describe families of simplicial complexes and combinatorial operations which allow for a systematic description of the LS-category. In particular, we characterize the LS-category of moment-angle complexes K{\mathcal{Z}{K}} over triangulated d-manifolds K for d≤2{d\leq 2}, as well as higher-dimensional spheres built up via connected sum, join, and vertex doubling operations. We show that the LS-category closely relates to vanishing of Massey products in HK){H (\mathcal{Z}_{K})}, and through this connection we describe first structural properties of Massey products in moment-angle manifolds. Some of the further applications include calculations of the LS-category and the description of conditions for vanishing of Massey products for moment-angle manifolds over fullerenes, Pogorelov polytopes and k-neighborly complexes, which double as important examples of hyperbolic manifolds.

Lusternik-Schnirelmann category, Massey products, moment-angle complex, non-Kähler manifolds, Polyhedral product, toric topology
0933-7741
1179-1205
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175

Beben, Piotr and Grbic, Jelena (2021) LS-category of moment-angle manifolds and higher order Massey products. Forum Mathematicum, 33 (5), 1179-1205. (doi:10.1515/forum-2021-0015).

Record type: Article

Abstract

Using the combinatorics of the underlying simplicial complex K, we give various upper and lower bounds for the Lusternik-Schnirelmann (LS) category of moment-angle complexes K{\mathcal{Z} {K}}. We describe families of simplicial complexes and combinatorial operations which allow for a systematic description of the LS-category. In particular, we characterize the LS-category of moment-angle complexes K{\mathcal{Z}{K}} over triangulated d-manifolds K for d≤2{d\leq 2}, as well as higher-dimensional spheres built up via connected sum, join, and vertex doubling operations. We show that the LS-category closely relates to vanishing of Massey products in HK){H (\mathcal{Z}_{K})}, and through this connection we describe first structural properties of Massey products in moment-angle manifolds. Some of the further applications include calculations of the LS-category and the description of conditions for vanishing of Massey products for moment-angle manifolds over fullerenes, Pogorelov polytopes and k-neighborly complexes, which double as important examples of hyperbolic manifolds.

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Accepted/In Press date: 25 July 2021
e-pub ahead of print date: 26 August 2021
Published date: 1 September 2021
Additional Information: Publisher Copyright: © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
Keywords: Lusternik-Schnirelmann category, Massey products, moment-angle complex, non-Kähler manifolds, Polyhedral product, toric topology

Identifiers

Local EPrints ID: 451580
URI: http://eprints.soton.ac.uk/id/eprint/451580
ISSN: 0933-7741
PURE UUID: 04785d18-624a-4902-9d6d-d9fc695c5bf6
ORCID for Jelena Grbic: ORCID iD orcid.org/0000-0002-7164-540X

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Date deposited: 12 Oct 2021 16:33
Last modified: 17 Mar 2024 06:52

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Contributors

Author: Piotr Beben
Author: Jelena Grbic ORCID iD

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