A bridge in between Poisson Geometry and Noncommutative Geometry through quantization processes.

Autor: Javier Alejandro Vega Huerta
The Lie brackets concept considered over manifolds has enriched that one of a manifold largely and fruitfully, even generalizing Symplectic structures by giving place to Poisson structures, so called Poisson Geometry. In the other hand, the not-that-old theory of Noncommutative Geometry is catching more and more attention as time pass from different realms of mathematics like Algebraic Geometry or Algebraic Topology. In this work, the main features of Poisson Geometry and Noncommutative Geometry are exposed. Then, both are linked through a quantization process, mainly, by deformation quantization.