The relation between local and global dual pairs
辛几何
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0310133,
title = {The relation between local and global dual pairs},
author = {James Montaldi and Juan-Pablo Ortega and Tudor S. Ratiu},
journal= {arXiv preprint arXiv:math/0310133},
year = {2007}
}
备注
9 pages. To appear in Mathematical Research Letters