2025/10/22 by Austin Christian, Christian, Austin, Shah, Tanushree
Mathematics · #57K33 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2510.19580
openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We develop a diagrammatic framework for applying the symplectic JSJ decomposition to exact/weak symplectic fillings of 3-dimensional contact manifolds. Namely, we apply the symplectic JSJ decomposition to a contact surgery diagram for some (Y,ζ), producing a finite collection of contact manifolds, also described diagrammatically, whose exact/weak symplectic fillings determine those of (Y,ζ). We apply this technique to recover known symplectic filling classifications for certain lens spaces and torus bundles, and also to provide an algorithm for classifying the exact/weak symplectic fillings of a large class of plumbed 3-manifolds.