Feynman Integral, Knot Invariant and Degree Theory of Maps

TL;DR

This paper demonstrates that the universal Vassiliev invariant derived from perturbative Chern-Simons theory is a genuine knot invariant, with the anomaly term shown to be zero, confirming its invariance.

Contribution

It proves that the anomaly in the Vassiliev invariant vanishes, establishing it as a true knot invariant without correction terms.

Findings

Anomaly considered by Bott and Taubes is zero

Vassiliev invariant is a genuine knot invariant

No correction term needed for the invariant

Abstract

The universal Vassiliev invariant from the perturbative Chern-Simons theory is actually a knot invariant without any correction term. The anomaly considered by Bott and Taubes is proved to be zero.