Picard groups in Poisson geometry
Symplectic Geometry
2007-05-23 v2 Differential Geometry
Abstract
We study isomorphism classes of symplectic dual pairs P <- S -> P-, where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres. For fixed P, these Morita self-equivalences of P form a group Pic(P) under a natural ``tensor product'' operation. We discuss this group in several examples and study variants of this construction for rings (the origin of the notion of Picard group), Lie groupoids, and symplectic groupoids.
Cite
@article{arxiv.math/0304048,
title = {Picard groups in Poisson geometry},
author = {Henrique Bursztyn and Alan Weinstein},
journal= {arXiv preprint arXiv:math/0304048},
year = {2007}
}
Comments
26 pages, to appear in special issue of Moscow Math. J. in honor of Pierre Cartier