Dirac structures, moment maps and quasi-Poisson manifolds
Differential Geometry
2007-05-23 v3 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian quasi-Poisson manifolds fit into this framework by constructing an ``inversion'' procedure relating quasi-Poisson bivectors to twisted Dirac structures.
Cite
@article{arxiv.math/0310445,
title = {Dirac structures, moment maps and quasi-Poisson manifolds},
author = {Henrique Bursztyn and Marius Crainic},
journal= {arXiv preprint arXiv:math/0310445},
year = {2007}
}
Comments
36 pages. Typos and signs fixed. To appear in Progress in Mathematics, Festschrift in honor of Alan Weinstein, Birkauser