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

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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