210219 Joao Nuno Mestre

Symplectic groupoids are Lie groupoids equipped with multiplicative symplectic forms, and serve as global counterparts to (integrable) Poisson manifolds, in the same way that Lie groups are global counterparts to Lie algebras.

In this talk I will present the construction of the deformation cohomology controlling deformations of symplectic groupoids, built out of the deformation complexes of a Lie groupoid and of a multiplicative form. We will see that it can be identified with the total complex of a sub double complex of the Bott-Shulman-Stasheff double complex.

I will then compute this cohomology in some particular cases (linear Poisson structures and proper groupoids), explain how to use it in a Moser path argument, and describe some relations to the deformation theory of the corresponding Poisson manifolds.

This is joint work with Cristian Cárdenas (UFF) and Ivan Struchiner (USP).