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We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the local Lie groupoid of a Lie algebroid, these formulas produce concrete integrations of several geometric stuctures defined infinitesimally. In particular, we obtain local integrations and non-degenerate realizations of Poisson, Nijenhuis–Poisson, Dirac, and Jacobi structures by local symplectic, symplectic-Nijenhuis, presymplectic, and contact groupoids, respectively.


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CABRERA, A., MĂRCUŢ, I. & SALAZAR, M.A. LOCAL FORMULAS FOR MULTIPLICATIVE FORMS. Transformation Groups 27, 371–401 (2022).

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