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Formality of Donaldson submanifolds

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An Erratum to this article was published on 30 June 2007

Abstract.

We introduce the concept of s–formal minimal model as an extension of formality. We prove that any orientable compact manifold M, of dimension 2n or (2n−1), is formal if and only if M is (n−1)–formal. The formality and the hard Lefschetz property are studied for the Donaldson submanifolds of symplectic manifolds constructed in [13]. This study permits us to show an example of a Donaldson symplectic submanifold of dimension eight which is formal simply connected and does not satisfy the hard Lefschetz theorem.

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain

    Marisa Fernández

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Vicente Muñoz

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  1. Marisa Fernández
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  2. Vicente Muñoz
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Correspondence to Marisa Fernández.

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An erratum to this article is available at http://dx.doi.org/10.1007/s00209-007-0208-2.

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Fernández, M., Muñoz, V. Formality of Donaldson submanifolds. Math. Z. 250, 149–175 (2005). https://doi.org/10.1007/s00209-004-0747-8

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