A JSJ-type decomposition theorem for symplectic fillings

2018/07/09 by Austin Christian, Christian, Austin, Michael M. Menke +1
Mathematics · #57R17 #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1807.03420

openalex publication_date 2018/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a JSJ-type decomposition theorem for splitting exact symplectic fillings of contact 3-manifolds along mixed tori -- these are convex tori satisfying a particular geometric condition. As an application, we show that if (M,ξ) is obtained from (S³,ξ_std) via Legendrian surgery along a knot which has been stabilized both positively and negatively, then (M,ξ) has a unique exact filling.

Related

• Splitting symplectic fillings
• Some applications of Menke's JSJ decomposition for symplectic fillings
• Mixed tori in contact surgery diagrams
• Symplectic fillings, contact surgeries, and Lagrangian disks
• A JSJ splitting for triangulated open 3-manifolds