Abstract:

Exponential maps, which are defined by geodesics, arise naturally in Differential Geometry. They are defined in an analytical way, but the infinity jets of geodesic exponential maps can be described by iterative algebraic formulas. Inspired by these formulas, we define and study formal exponential maps for Z-graded manifolds. As an application, we obtain a new construction of Dolgushev-Fedosov resolutions in deformation quantization.