Symplectic torus bundles and group extensions
| dc.creator | Kahn, Peter J. | |
| dc.date | 2004-05-06 | |
| dc.date.accessioned | 2026-07-07T05:07:59Z | |
| dc.date.available | 2026-07-07T05:07:59Z | |
| dc.description | Symplectic torus bundles $ξ:T^{2}\to E\to B$ are classified by the second cohomology group of $B$ with local coefficients $H_{1}(T^{2})$. 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. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0405109 | |
| dc.identifier | http://arxiv.org/abs/math/0405109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71081 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57R17; 20K35 | |
| dc.title | Symplectic torus bundles and group extensions | |
| dc.type | text |