Almost Lagrangian obstruction |
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Authors: | Daniele Sepe |
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Institution: | School of Mathematics and Maxwell Institute for Mathematical Sciences, The University of Edinburgh, James Clerk Maxwell Building, King?s Buildings, Edinburgh, EH9 3JZ, UK |
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Abstract: | 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 in Zung (2003) 16]. It is shown that this obstruction (namely, the homomorphism D of Dazord and Delzant (1987) 4] and Zung (2003) 16]) 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 explicit examples are calculated, thus providing the first examples of non-trivial Lagrangian obstructions. |
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Keywords: | MSC: 37J35 37J05 57R17 70H06 |
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