Computation of Kontsevich Weights of Connection and Curvature Graphs for Symplectic Poisson Structures

Abstract

We give an explicit computation of weights of Kontsevich graphs which arise from connection and curvature terms within the globalization picture as in [12] for symplectic manifolds. Moreover, we consider the case of a cotangent bundle, which will simplify the curvature expression significantly. Contents 1. Introduction 1.1. Motivation 1.2. Notions of Formal Geometry Acknowledgements 2. Computation of Kontsevich Weights 2.1. Case 1: No Boundary Vertices 2.2. Case 2: One Boundary Vertex 2.3. Case 3: Two Boundary Vertices 3. Including the Weights 3.1. The Product P (Tφ * π) The Connection 1-form1 Endowed with the zero differential and the Schouten-Nijenhuis bracket.2 Endowed with the Hochschild differential and the Gerstenhaber bracket.