Rationality Results for the Configuration Space Integral of Knots

The perturbative Chern-Simons theory for knots in Euclidean space is a linear combination of integrals on configuration spaces. This has been successively studied by Bott and Taubes, Altschuler and Freidel, and Yang. We study it again in terms of degree theory, with a new choice of compactification. This paper is self-contained and proves some old and new results, especially a rationality result with some information on the denominators.