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The Quarterly Journal of Mathematics Advance Access published online on February 10, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap003
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

SEMI-GLOBAL INVARIANTS OF PIECEWISE SMOOTH LAGRANGIAN FIBRATIONS

Ricardo Castaño-Bernard{dagger}

Mathematics Department, Kansas State University, 138 Cardwell Hall, Manhattan, KS 66506, Kansas

Diego Matessi {ddagger}

Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale, Via Bellini 25/G, I-15100 Alessandria, Italy

{dagger} Corresponding author. E-mail: rcastano{at}math.ksu.edu

Received 1 August 2008;
  Abstract

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 co-ordinates to these fibrations by defining certain invariants which give a semi-global classification of germs of stitched fibrations. We then describe stitched fibrations with monodromy in terms of these invariants.

{ddagger} E-mail: matessi{at}unipm.it


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