Luttinger surgery and Kodaira dimension

2011/08/02 by Chung-I Ho, Tianjun Li, Tian-Jun Li +2 · 1 citation
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.1108.0479

23 pages; to appear in Asian Journal of Mathematics

openalex publication_date 2011/08/02 · arxiv created 2011/08/03 · arxiv updated 2011/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we show that the Lagrangian Luttinger surgery preserves the symplectic Kodaira dimension. Some constraints on Lagrangian tori in symplectic four manifolds with non-positive Kodaira dimension are also derived.

Citations

• Some open questions about symplectic 4-manifolds, singular plane curves, and braid group factorizations

Cited by

• Simply Connected Symplectic Calabi-Yau 6-Manifolds
• Distinguishing closed 4-manifolds by slicing

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