The Kontsevich weight of a wheel with spokes pointing outward

TL;DR

This paper computes the Kontsevich weight of a specific wheel graph with outward spokes using elementary methods, relating it to modified Bernoulli numbers, and confirms previous results obtained by more advanced techniques.

Contribution

It provides an elementary derivation of the Kontsevich weight for a wheel with outward spokes, connecting it to Bernoulli numbers, and verifies earlier findings by Torossian and Willmacher.

Findings

Kontsevich weight expressed in terms of modified Bernoulli numbers

Elementary methods successfully reproduce previous complex results

Confirms earlier unpublished and recent computations

Abstract

This is a companion note to ``Hochschild cohomology and Atiyah classes'' by Damien Calaque and the author. Using elementary methods we compute the Kontsevich weight of a wheel with spokes pointing outward. The result is in terms of modified Bernouilli numbers. The same result had been obtained earlier by Torossian (unpublished) and also recently by Thomas Willmacher using more advanced methods.