Non-trivial higher Massey products in moment-angle complexes

As part of various obstruction theories, non-trivial Massey products have been studied in symplectic and complex geometry, commutative algebra topology for a long time. We introduce general approach to constructing the cohomology moment-angle complexes, using homotopy theoretical combinatorial methods. Our sets unifying way higher arbitrary cohomological classes generalises all existing examples complexes. result, we obtain explicit constructions infinitely many non-formal manifolds that appear topology, geometry algebraic geometry.