2003/10/31 by James Montaldi, Juan-Pablo Ortega, Tudor S. Ratiu
Mathematics · #math.SG #msc:53Dxx #msc:53D17 #msc:70Hxx
published as Math. Res. Lett. 11 (2004), no. 2-3, 355--363 · 9 pages. To appear in Mathematical Research Letters
arxiv created 2004/04/26 · arxiv updated 2009/12/01
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.