Noncommutative Chern-Weil theory and the combinatorics of wheeling

Abstract

This work applies the ideas of Alekseev and Meinrenken's noncommutative Chern-Weil theory to describe a completely combinatorial and constructive proof of the wheeling theorem. In this theory, the crux of the proof is, essentially, the familiar demonstration that a characteristic class does not depend on the choice of connection made to construct it. To a large extent, this work may be viewed as an exposition of the details of some of Alekseev and Meinrenken's theory written for Kontsevich integral specialists. Our goal was a presentation with full combinatorial detail in the setting of Jacobi diagrams. To achieve this goal, certain key algebraic steps required replacement with substantially different combinatorial arguments.