English

Existence of conformal symplectic foliations on closed manifolds

Symplectic Geometry 2021-11-02 v1 Geometric Topology

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.

Keywords

Cite

@article{arxiv.2111.00550,
  title  = {Existence of conformal symplectic foliations on closed manifolds},
  author = {Fabio Gironella and Lauran Toussaint},
  journal= {arXiv preprint arXiv:2111.00550},
  year   = {2021}
}

Comments

38 pages, 6 figures