 

Peter J. Kahn
Symplectic torus bundles and group extensions


Published: 
February 3, 2005

Keywords: 
symplectic, fibre bundle, torus, group extension, localization 
Subject: 
57R17, 20K35, 53D05 


Abstract
Symplectic torus bundles ξ:T^{2}→ E→ 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 groupextensiontheoretic construction of J. Huebschmann, 1981. A key ingredient is the
notion of fibrewiselocalization.


Author information
Dept. of Math., Malott Hall, Cornell U., Ithaca, NY 14850
kahn@math.cornell.edu
http://www.math.cornell.edu/~kahn/

