2004/05/06 by Peter J. Kahn, Kahn, Peter J. · 3 citations
Mathematics · #20K35 #57R17 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AT #math.SG #msc:20K35 #msc:57R17
paper · pdf · doi:10.48550/arxiv.math/0405109
18 pages
arxiv created 2004/05/06 · openalex publication_date 2004/05/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Symplectic torus bundles ξ:T2→ E→ B are classified by the second cohomology group of B with local coefficients H1(T2). For B a compact, orientable surface, the main theorem of this paper gives a necessary and sufficient condition on the cohomology class corresponding to ξ for E to admit a symplectic structure compatible with the symplectic bundle structure of ξ : namely, that it be a torsion class. The proof is based on a group-extension-theoretic construction of J. Huebschmann (Sur les premieres differentielles de la suite spectrale cohomologique d'une extension de groupes, C.R. Acad. Sc. Paris, Serie A, tome 285, 28 novembre 1977, 929-931). A key ingredient is the notion of fibrewise-localization.