Unknottedness of symplectic submanifold fillings

2025/06/07 by Zhengyi Zhou, Zhou, Zhengyi
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic and Operator Theory #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2506.06807

openalex publication_date 2025/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that any symplectic filling of the standard contact submanifold (\mathbbS^2n-1,ξ_std) of (\mathbbS²ⁿ⁺¹,ξ_std) in (\mathbbDⁿ⁺¹,ω_std) is smoothly unknotted if n≥ 2. We also give a self-contained proof of the Siefring intersection formula between punctured holomorphic curves and holomorphic hypersurfaces used in the proof using the L-simple setup of Bao-Honda.

Citations

• Contact homology and linearization without dga homotopies
• Bourgeois' contact manifolds are tight
• Stabilization of divisors in high-dimensional contact manifolds
• An algebraic generalization of Giroux's criterion
• A note on contact manifolds with infinite fillings
• Holomorphic curves in the presence of holomorphic hypersurface foliations
• Non-simplicity of isocontact embeddings in all higher dimensions
• Contact 3-manifolds, holomorphic curves and intersection theory
• Semi-global Kuranishi charts and the definition of contact homology
• Periodic Symplectic Cohomologies
• S¹-equivariant symplectic homology and linearized contact homology
• Effect of Legendrian Surgery
• A biased view of symplectic cohomology
• Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces
• Introduction to Symplectic Field Theory
• Symplectic manifolds with contact type boundaries

Related

• Tight contact structures with no symplectic fillings
• A few remarks about symplectic filling
• Fillability obstructions for high-dimensional confoliations
• Splitting symplectic fillings
• Symplectic fillings of virtually overtwisted contact structures on lens spaces