Stability and Existence of Surfaces in Symplectic 4-Manifolds with b⁺=1

2014/07/03 by Josef G. Dorfmeister, Tianjun Li, Dorfmeister, Josef G. +3 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1407.1089

openalex publication_date 2014/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish various stability results for symplectic surfaces in symplectic 4-manifolds with b⁺=1. These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify negative symplectic spheres in symplectic 4-manifolds with κ=-∞. This involves the explicit construction of spheres in rational manifolds via a new construction technique called the tilted transport.

Cited by

• Finite group actions on symplectic Calabi-Yau 4-manifolds with b₁>0

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