LS-category of moment-angel manifolds and Massey products

     We give various bounds for the Lusternik-Schnirelmann category of moment-angle complexes ZKZK and show how this relates to vanishing of Massey products in H∗(ZK)H∗(ZK). In particular, we characterise the Lusternik-Schnirelmann category of moment-angle manifolds ZKZK over triangulated dd-spheres KK for d≤2d≤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 KK, the cup product length of H∗(ZK)H∗(ZK), as well as a certain Massey products. Some of the applications include calculations of the Lusternik-Schnirelmann category and the description of conditions for vanishing of Massey products for moment-angle complexes over fullerenes and kk-neighbourly complexes.

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