Gauge equivalence of Dirac structures and symplectic groupoids

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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.
22 pages. Corrections made in Section 6.1, typos fixed and one reference added. To appear in Ann. Inst. Fourier

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Symplectic Geometry, Mathematical Physics, Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/63312

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0202099
 http://arxiv.org/abs/math/0202099

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arXiv