Computation of Kontsevich Weights of Connection and Curvature Graphs for Symplectic Poisson Structures
Abstract
We give a detailed explicit computation of weights of Kontsevich graphs which arise from connection and curvature terms within the globalization picture for the special case of symplectic manifolds. We will show how the weights for the curvature graphs can be explicitly expressed in terms of the hypergeometric function as well as by a much simpler formula combining it with the explicit expression for the weights of its underlined connection graphs. Moreover, we consider the case of a cotangent bundle, which will simplify the curvature expression significantly.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 DOI:
 10.48550/arXiv.1912.08742
 arXiv:
 arXiv:1912.08742
 Bibcode:
 2019arXiv191208742M
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Differential Geometry;
 Mathematics  Quantum Algebra;
 Mathematics  Symplectic Geometry;
 81S10;
 53D55;
 53D17;
 81T18
 EPrint:
 30 pages, 14 figures, to appear in Adv. Theor. Math. Phys