Abstract
We study the existence of symplectic and conformal symplectic (codimension-1) foliations on closed manifolds of dimension ≥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.
| Original language | English |
|---|---|
| Pages (from-to) | 2281-2335 |
| Number of pages | 55 |
| Journal | Mathematische Annalen |
| Volume | 390 |
| Issue number | 2 |
| Early online date | 3 Feb 2024 |
| DOIs | |
| Publication status | Published - Oct 2024 |
Bibliographical note
Publisher Copyright:© The Author(s) 2024.
Funding
Throughout the preparation of this work, the second author has been supported by both the F.R.S-FNRS and the FWO under the Excellence of Science programme (grant No. 30950721), and the Dutch Research Council (NWO) on the project \u201Cproper Fredholm homotopy theory\u201D (OCENW.M20.195) of the research programme Open Competition ENW M20-3.
| Funders | Funder number |
|---|---|
| Fonds De La Recherche Scientifique - FNRS | |
| Horizon 2020 Framework Programme | 772479 |
| Fonds Wetenschappelijk Onderzoek | 30950721 |
| Nederlandse Organisatie voor Wetenschappelijk Onderzoek | OCENW.M20.195 |
Keywords
- 53C12
- 53D05
- 53D10
- 57R17
- 57R30