Deformations of symplectic groupoids
Presenting author: Joćo Nuno Mestre
A central problem in geometry is that of understanding the behaviour of geometric structures
under deformations. Each class of geometric structures comes with its deformation theory,
generally including a cohomology theory that controls such deformations. The Moser trick
from symplectic geometry is a good illustration of a technique by which one can prove
rigidity results through cohomological arguments.
In this talk we discuss deformations of Lie groupoids and introduce the cohomology which controls them.
We will explain how to use the deformation cohomology in order to prove rigidity and normal
form results for compact and for proper Lie groupoids.
Finally, we explain how the general theory behaves in the case of symplectic groupoids
- these are the Lie groupoids that serve as global counterparts of integrable Poisson manifolds.
This talk is based on joint work with Marius Crainic and Ivan Struchiner.
Click here to access the slides.