LS-category of moment-angle manifolds, Massey products, and a generalisation of the Golod property

Abstract

This paper is obtained as as synergy of homotopy theory, commutative algebra and combinatorics. We give various bounds for the Lusternik-Schnirelmann category of moment-angle complexes and show how this relates to vanishing of Massey products in Tor+R[v1,...,vn] (R [K], R) for the Stanley-Reisner ring R[K]. In particular, we characterise the Lusternik-Schnirelmann category of moment-angle manifolds ZK over triangulated d-spheres K for d ≤ 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 generalisation of the Golod property. As an application, we describe conditions for vanishing of Massey products in the case of fullerenes and k-neighbourly complexes