2002/02/12 by Henrique Bursztyn, Bursztyn, Henrique, Olga Radko +1
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.DG #math.MP #math.SG
paper · pdf · doi:10.48550/arxiv.math/0202099
22 pages. Corrections made in Section 6.1, typos fixed and one reference added. To appear in Ann. Inst. Fourier
arxiv created 2002/10/21 · arxiv updated 2009/11/30
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.