On the formality and strong Lefschetz property of symplectic manifolds – Erratum

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Professor Vicente Muñoz kindly informed us that there is an inaccuracy in Lemma 3.5 of [1]. The correct statement of Lemma 3.5 is now that the fundamental group π₁(X′) of the manifold X′ is Z, since the monodromy coming from φ₈ does not imply that g₄ = g₄⁻¹. Therefore, what we have actually constructed in Section 3 of [1] is a closed non-formal 8-dimensional symplectic manifold with π₁ = Z whose triple Massey product is non-zero, so that the simply-connectedness in Theorem 1.1 should be dropped. As far as we know, the existence of a simply connected closed non-formal 8-dimensional symplectic manifold whose triple Massey product is non-zero still remains an open question. All other main results, especially Theorem 1.2 and Corollary 1.3, in [1] are not affected by this mistake. Furthermore, the stability of the non-formality under a finite covering as in Subsection 3.3 holds in general. We want to thank Professor Muñoz for his careful reading.