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

Using the combinatorics of the underlying simplicial complex , we give various upper and lower bounds for the Lusternik–Schnirelmann (LS) category of moment-angle complexes . We describe families of simplicial complexes and combinatorial operations which allow for a systematic description of the LS-...

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Bibliographic Details
Published inForum mathematicum Vol. 33; no. 5; pp. 1179 - 1205
Main Authors Beben, Piotr, Grbić, Jelena
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.09.2021
Walter de Gruyter GmbH
Subjects
05E40
32Q55
55M30
55U10
Combinatorial analysis
Lower bounds
Lusternik–Schnirelmann category
Massey products
moment-angle complex
non-Kähler manifolds
Polyhedral product
Polytopes
toric topology
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Summary:Using the combinatorics of the underlying simplicial complex , we give various upper and lower bounds for the Lusternik–Schnirelmann (LS) category of moment-angle complexes . 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 over triangulated -manifolds for , 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 , 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 -neighborly complexes, which double as important examples of hyperbolic manifolds.
ISSN:0933-7741
1435-5337
DOI:10.1515/forum-2021-0015