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arXiv · 2111.00550

Existence of conformal symplectic foliations on closed manifolds

Fabio Gironella·Lauran Toussaint
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Abstract

We consider the existence of symplectic and conformal symplectic codimension-one foliations on closed manifolds of dimension at least 5. Our main theorem, based on a recent result by Bertelson-Meigniez, states that in dimension at least 7 any almost contact structure is homotopic to a conformal symplectic foliation. In dimension 5 we construct explicit conformal symplectic foliations on every closed, simply-connected, almost contact manifold, as well as honest symplectic foliations on a large subset of them. Lastly, via round-connected sums, we obtain, on closed manifolds, examples of conformal symplectic foliations which admit a linear deformation to contact structures.

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Fabio Gironella, Lauran Toussaint. 2021-10-31. Existence of conformal symplectic foliations on closed manifolds. https://arxiv.org/abs/2111.00550

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