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

Published online by Cambridge University Press:  01 July 2009

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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.

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Erratum
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Copyright © Cambridge Philosophical Society 2009

References

REFERENCE

[1]Hwang, T. K. and Kim, J. H., On the the formality and strong Lefschetz property of symplectic manifolds. Math. Proc. Camb. Phil. Soc. 145 (2008), 363377.CrossRefGoogle Scholar