Mathematical Research Letters

Volume 11, Issue 3, May 2004 pp. 355-363.

The relation between local and global dual pairs

Authors: James Montaldi, Juan-Pablo Ortega and Tudor S. Ratiu
Author institution: UMIST, Universitè de Franche-Comtè, and Ècole Polytechnique

Summary: 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.

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