English

Formality of Donaldson submanifolds

Symplectic Geometry 2007-05-23 v3 Algebraic Topology

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 symplectic manifolds constructed by Donaldson with asymptotically holomorphic techniques. This study permits us to show an example of a Donaldson symplectic manifold of dimension eight which is formal simply connected and does not satisfy the hard Lefschetz theorem.

Keywords

Cite

@article{arxiv.math/0211017,
  title  = {Formality of Donaldson submanifolds},
  author = {Marisa Fernández and Vicente Muñoz},
  journal= {arXiv preprint arXiv:math/0211017},
  year   = {2007}
}

Comments

24 pages, no figures, Latex2e; v3. statement of Lemma 2.7 corrected

R2 v1 2026-07-22T16:48:58.741Z