Almost Lagrangian obstruction
Copyright policy )Almost Lagrangian obstruction
The aim of this paper is to describe the obstruction for an almost Lagrangian fibration to be Lagrangian, a problem which is central to the classification of Lagrangian fibrations and, more generally, to understanding the obstructions to carry out surgery of integrable systems, an idea introduced by Zung. It is shown that this obstruction (namely, the homomorphism of Dazord and Delzant) is related to the cup product in cohomology with local coefficients on the base space B of the fibration. The map is described explicitly and some examples are calculated, thus providing the first examples of non-trivial Lagrangian obstructions.
17 pages, to appear in Diff. Geom. Appl
- University of Edinburgh United Kingdom
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Symplectic and contact topology in high or arbitrary dimension, Lagrangian fibrations, 37J35, 37J05, 57R17, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Relations of dynamical systems with symplectic geometry and topology, Computational Theory and Mathematics, Mathematics - Symplectic Geometry, completely integrable Hamiltonian systems, FOS: Mathematics, Symplectic Geometry (math.SG), Geometry and Topology, Completely integrable Hamiltonian systems, Analysis
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Symplectic and contact topology in high or arbitrary dimension, Lagrangian fibrations, 37J35, 37J05, 57R17, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Relations of dynamical systems with symplectic geometry and topology, Computational Theory and Mathematics, Mathematics - Symplectic Geometry, completely integrable Hamiltonian systems, FOS: Mathematics, Symplectic Geometry (math.SG), Geometry and Topology, Completely integrable Hamiltonian systems, Analysis
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