New York Journal of Mathematics
Volume 11 (2005) 35-55


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

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, 1981. A key ingredient is the notion of fibrewise-localization.

Author information

Dept. of Math., Malott Hall, Cornell U., Ithaca, NY 14850