Formality of Donaldson submanifolds
By M. Fernández, V. Muñoz. 2002
76 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a37dee9d91bf931649893e6aabb8520c61488402
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In Geometry and Topology
Citations in the corpus
- An 8-dimensional nonformal, simply connected, symplectic manifold (2005, background): “c blow-up [16]. They raise the question of the existence of non-formal simply connected compact symplectic manifolds of dimension 8. The techniques of construction of symplectic manifolds used so far [1, 3, 6, 7, 11, 14, 21, 22] have not proved fruitful when addressing this problem. In this note, we”
- On Low-Dimensional Solvmanifolds (2009, background): “The next theorem shows the reason for defining s-formality: in certain cases s-formality is sufficient for a manifold to be formal. Theorem 1.1.3 ([ 21, Theorem 3.1 ]).”