Non-trivial higher Massey products in moment-angle complexes

Formality and finiteness in rational homotopy theory

“…In this situation, Corollary 10.28 no longer applies, since the inclusion-induced homomorphism 1 ( 2 , Q) → 1 ( 1 , Q) is not surjective. In fact, there are infinite families of simplicial complexes for which * (Z , Q) has non-vanishing Massey products, and thus Z is non-formal, see [9], [38], [64]. If is an -vertex triangulation of , then Z is a closed manifold of dimension + + 1.…”

“…In general, though, the complement of a complex subspace arrangement need not be formal. For instance, the polyhedral product constructions of [9], [38], [64] mentioned in Section 10.8 yield coordinate subspace arrangements whose complements admit non-trivial Massey products over the rationals.…”