2004/10/28 by Weimin Chen, Chen, Weimin
Mathematics · #57M60 #57R17 #57R57 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematics and Applications #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:57M60 #msc:57R17 #msc:57R57
paper · pdf · doi:10.48550/arxiv.math/0410608
27 pages, no figures, expository article, improved exposition, accepted for publication in Proceedings of Conference on Geometry and Topology of Manifolds, McMaster University, May 14-18, 2004
openalex publication_date 2004/10/28 · arxiv created 2005/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main purpose of this paper is to summarize the basic ingredients, illustrated with examples, of a pseudoholomorphic curve theory for symplectic 4-orbifolds. These are extensions of relevant work of Gromov, McDuff and Taubes on symplectic 4-manifolds concerning pseudoholomorphic curves and Seiberg-Witten theory. They form the technical backbone of the proof that a symplectic s-cobordism of elliptic 3-manifolds (with a canonical contact structure on the boundary) is smoothly a product. One interesting feature of the theory is that existence of pseudoholomorphic curves gives certain restrictions on the singular points of the 4-orbifold contained by the pseudoholomorphic curves. In the last section, we discuss applications (or potential ones) of the theory in some other problems such as symplectic finite group actions on 4-manifolds, symplectic circle actions on 6-manifolds, and algebraic surfaces with quotient singularities.