Non-commutative Chern-Weil Theory and the Combinatorics of Wheeling

Details Non-commutative Chern-Weil Theory and the Combinatorics of Wheeling Non-commutative Chern-Weil Theory and the Combinatorics of Wheeling

2006-12-21

arxiv.org/abs/math/0612653v3

Mathematics

Quantum Algebra

45 pages. Revised. An outline added to the introduction. (v3: Technical problem with the pdf of v2 fixed.)

Scientific paper

This work applies the ideas of Alekseev and Meinrenken's Non-commutative 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.

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