Existence of symplectic structures on torus bundles over surfaces

2003/10/17 by R. Walczak, Rafal Walczak, Walczak, Rafal · 2 citations
Mathematics · #53D05 #55R20 #57R57 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG #msc:53D05 #msc:55R20 #msc:57R57

paper · pdf · doi:10.48550/arxiv.math/0310261

Changed content; Latex; Comments are welcome

openalex publication_date 2003/10/17 · arxiv created 2004/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E be the total space of a locally trivial torus bundle over the surface Σ_g of genus g>1. Using the Seiberg--Witten theory and spectral sequences we prove that E carries a symplectic structure if and only if the homology class of the fiber [T²] is nonzero in H₂(E,R).

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