Symplectic forms on trisected 4-manifolds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929268023361536 |
|---|---|
| author | Lambert-Cole, Peter |
| author_facet | Lambert-Cole, Peter |
| contents | Previously work of the author with Meier and Starkston showed that every closed symplectic manifold $(X,ω)$ with a rational symplectic form admits a trisection compatible with the symplectic topology. In this paper, we describe the converse direction and give explicit criteria on a trisection of a closed, smooth 4-manifold $X$ that allows one to construct a symplectic structure on $X$. Combined, these give a new characterization of 4-manifolds that admit symplectic structures. This construction motivates several problems on taut foliations, the Thurston norm and contact geometry in 3-dimensions by connecting them to questions about the existence, classification and uniqueness of symplectic structures on 4-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13576 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Symplectic forms on trisected 4-manifolds Lambert-Cole, Peter Geometric Topology Previously work of the author with Meier and Starkston showed that every closed symplectic manifold $(X,ω)$ with a rational symplectic form admits a trisection compatible with the symplectic topology. In this paper, we describe the converse direction and give explicit criteria on a trisection of a closed, smooth 4-manifold $X$ that allows one to construct a symplectic structure on $X$. Combined, these give a new characterization of 4-manifolds that admit symplectic structures. This construction motivates several problems on taut foliations, the Thurston norm and contact geometry in 3-dimensions by connecting them to questions about the existence, classification and uniqueness of symplectic structures on 4-manifolds. |
| title | Symplectic forms on trisected 4-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2212.13576 |