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- Title
Symplectic embeddings in infinite codimension.
- Authors
Araújo, Manuel; Granja, Gustavo
- Abstract
Let X be a union of a sequence of symplectic manifolds of increasing dimension and let M be a manifold with a closed 2-form ω<inline-graphic></inline-graphic>. We use Tischler’s elementary method for constructing symplectic embeddings in complex projective space to show that the map from the space of embeddings of M in X to the cohomology class of ω<inline-graphic></inline-graphic> given by pulling back the limiting symplectic form on X is a weak Serre fibration. Using the same technique we prove that, if b2(M)<∞<inline-graphic></inline-graphic>, any compact family of closed 2-forms on M can be obtained by restricting a standard family of forms on a product of complex projective spaces along a family of embeddings.
- Subjects
SYMPLECTIC manifolds; EMBEDDINGS (Mathematics); COHOMOLOGY theory; MATHEMATICAL sequences; MATHEMATICAL analysis
- Publication
Journal of Homotopy & Related Structures, 2018, Vol 13, Issue 2, p461
- ISSN
2193-8407
- Publication type
Article
- DOI
10.1007/s40062-017-0189-8