Integrable system vs lagrangian fibration












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Every complete integrable system $I:M rightarrow mathbb{R}^n$ is a regular langrangian fibration on a dense subset of the symplectic manifold $M$.



It is also known that locally every lagrangian fibration looks locally as a complete integrable system.



I'm left the wonder what obstructions arise when we ask the question "does this lagrangian fibration match a complete integrable system?"










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    $begingroup$


    Every complete integrable system $I:M rightarrow mathbb{R}^n$ is a regular langrangian fibration on a dense subset of the symplectic manifold $M$.



    It is also known that locally every lagrangian fibration looks locally as a complete integrable system.



    I'm left the wonder what obstructions arise when we ask the question "does this lagrangian fibration match a complete integrable system?"










    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      Every complete integrable system $I:M rightarrow mathbb{R}^n$ is a regular langrangian fibration on a dense subset of the symplectic manifold $M$.



      It is also known that locally every lagrangian fibration looks locally as a complete integrable system.



      I'm left the wonder what obstructions arise when we ask the question "does this lagrangian fibration match a complete integrable system?"










      share|cite|improve this question









      $endgroup$




      Every complete integrable system $I:M rightarrow mathbb{R}^n$ is a regular langrangian fibration on a dense subset of the symplectic manifold $M$.



      It is also known that locally every lagrangian fibration looks locally as a complete integrable system.



      I'm left the wonder what obstructions arise when we ask the question "does this lagrangian fibration match a complete integrable system?"







      symplectic-geometry fibration integrable-systems






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 16 at 14:29









      NetivoluNetivolu

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