Abstract

In this talk, the idea is to describe with some detail certain singular cotangent (algebroid) homotopies, associated to a Poisson manifold M, which appear as a semiclassical limit in the Poisson Sigma Model (PSM). To that end, first, we will review the heuristic motivation for the PDEs that define these homotopies and their role in quantization. We then proceed to describe the solutions and relate them to certain triangles in an integrating groupoid. The final aim is to show how these homotopies, when fed into a PSM action functional, yield a generating function for the structure of a (local) symplectic groupoid integrating the underlying Poisson M.