The relation between local and global dual pairs

James Montaldi, Juan Pablo Ortega, Tudor S. Ratiu

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    In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage from local to global one needs a connected fiber hypothesis (this is well known), while the converse requires a dimension condition (which appears not to be known). We also provide examples illustrating the necessity of the extra conditions.
    Original languageEnglish
    Pages (from-to)355-363
    Number of pages8
    JournalMathematical Research Letters
    Issue number2-3
    Publication statusPublished - Mar 2004


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