Symplectic embeddings in infinite codimension

Manuel Araujo; Gustavo Granja

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arXiv · 1404.2433

Symplectic embeddings in infinite codimension

Manuel Araujo·Gustavo Granja

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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 $ω$. 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 $ω$ given by pulling back the limiting symplectic form on $X$ is a weak Serre fibration. Using the same technique we prove that, if $b_2(M)<\infty$, 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.

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BibTeX RIS

Manuel Araujo, Gustavo Granja. 2016-03-04. Symplectic embeddings in infinite codimension. https://arxiv.org/abs/1404.2433

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