Advances in Theoretical and Mathematical Physics

Volume 25 (2021)

Number 5

Computation of Kontsevich weights of connection and curvature graphs for symplectic Poisson structures

Pages: 1325 – 1365



Nima Moshayedi (Institut für Mathematik, Universität Zürich, Switzerland)

Fabio Musio (Institut für Mathematik, Universität Zürich, Switzerland)


We give a detailed explicit computation of weights of Kontsevich graphs which arise from connection and curvature terms within the globalization picture as in [12] 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.

This research was (partly) supported by the NCCR SwissMAP, funded by the Swiss National Science Foundation, and by the SNF grant No. 200020 172498/1.

Published 17 June 2022