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

  • Piotr Beben and Jelena Grbić EMAIL logo
Published/Copyright: August 26, 2021

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 𝒵K. 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 𝒵K over triangulated d-manifolds K for d2, 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 H*(𝒵K), 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.


Communicated by Frederick R. Cohen


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Received: 2019-10-29
Revised: 2021-06-21
Published Online: 2021-08-26
Published in Print: 2021-09-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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