Semi-global invariants of piecewise smooth Lagrangian fibrations

Details Semi-global invariants of piecewise smooth Lagrangian fibrations Semi-global invariants of piecewise smooth Lagrangian fibrations

2006-03-21

arxiv.org/abs/math/0603498v1

Mathematics

Symplectic Geometry

34 pages, 2 figures. This is a slightly different version from the one appeared as IHES preprint at http://www.ihes.fr/PREPR

Scientific paper

10.1093/qmath/hap003

We study certain types of piecewise smooth Lagrangian fibrations of smooth symplectic manifolds, which we call stitched Lagrangian fibrations. We extend the classical theory of action-angle coordinates to these fibrations by encoding the information on the non-smoothness into certain invariants consisting, roughly, of a sequence of closed 1-forms on a torus. The main motivation for this work is given by the piecewise smooth Lagrangian fibrations previously constructed by the authors (in Some piece-wise smooth Lagrangian fibrations, http://seminariomatematico.dm.unito.it/rendiconti/63-3.html), which topologically coincide with the local models used by M. Gross in his paper "Topological Mirror Symmetry", http://arxiv.org/abs/math.AG/9909015..

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