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We give a combinatorial classification of non-trivial triple Massey products of three dimensional classes in the cohomology of a moment-angle complex Z K . This result improves on [5, Theorem 6.1.1] by considering triple Massey products with non-trivial indeterminacy.

We describe two different systematic constructions of new nontrivial higher Massey products in the cohomology of moment-angle complexes, using homotopy theory and combinatorial operations. These constructions in conjunction detect non-trivial higher Massey products in the cohomology of moment-angle manifolds corresponding to polytopes such as families of graph associahedra. Our constructions use stellar subdivisions and edge contractions on simplicial complexes. These operations do not change the homotopy type of a simplicial complex, but do change the combinatorics, which changes the corresponding moment-angle complex.

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