Poisson geometry, monoidal Fukaya categories, and commutative Floer cohomology rings (Q6618780)

The paper studies the theory of symplectic groupoids from the viewpoint of Fukaya category. Symplectic groupoids are geometric objects appearing in Poisson geometry, which are powerful tools to develop the theory of reduction and momentum maps, quantization, and so on. After reviewing basic knowledge on symplectic groupoids, the paper explicates how Fukaya category is constructed from a given symplectic groupoid and illustrates many examples of monoidal Fukaya categories with symplectic groupoids.