2022/12/27 by Peter Lambert‐Cole, Lambert-Cole, Peter
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2212.13576
openalex publication_date 2022/12/27 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28
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.