P.O. Box 407, 9700 AK Groningen, The Netherlands
Institute for Mathematics and Computer Science, University of Groningen
Lukina O. V., Takens F., Broer H. W.
Global properties of integrable Hamiltonian systems
2008, vol. 13, no. 6, pp. 602-644
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our approach, which uses simple ideas from differential geometry and algebraic topology, reveals the fundamental role of the integer affine structure on the base space of these bundles. We provide a geometric proof of the classification of Lagrangian bundles with fixed integer affine structure by their Lagrange class.