Gauge equivalence of Dirac structures and symplectic groupoids
Symplectic Geometry
2007-05-23 v3 Mathematical Physics
Differential Geometry
math.MP
Abstract
We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent integrable Poisson structures are Morita equivalent. As an example, we study certain generic sets of Poisson structures on Riemann surfaces: we find complete gauge-equivalence invariants for such structures which, on the 2-sphere, yield a complete invariant of Morita equivalence.
Keywords
Cite
@article{arxiv.math/0202099,
title = {Gauge equivalence of Dirac structures and symplectic groupoids},
author = {Henrique Bursztyn and Olga Radko},
journal= {arXiv preprint arXiv:math/0202099},
year = {2007}
}
Comments
22 pages. Corrections made in Section 6.1, typos fixed and one reference added. To appear in Ann. Inst. Fourier