(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 \(\zk\). We describe families of simplicial complexes and combinatorial operations which allow for a systematic descriptio...

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Bibliographic Details
Published inarXiv.org
Main Authors Beben, Piotr, Grbić, Jelena
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.01.2021
Subjects
Combinatorial analysis
Combinatorics
Fullerenes
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Summary: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 \(\zk\). We describe families of simplicial complexes and combinatorial operations which allow for a systematic description of the LS category. In particular, we characterise the LS category of moment-angle complexes \(\zk\) over triangulated \(d\)-manifolds \(K\) for \(d\leq 2\), as well as higher dimension spheres built up via connected sum, join, and vertex doubling operations. %This characterisation is given in terms of the combinatorics of \(K\), the cup product length of \(H^*(\zk)\), as well as a certain Massey products. We show that the LS category closely relates to vanishing of Massey products in \(H^*(\zk)\) and through this connection we describe first structural properties of Massey products in moment-angel manifolds. Some of 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 \(k\)-neighbourly complexes, which double as important examples of hyperbolic manifolds.
ISSN:2331-8422