On Denominators of the Kontsevich Integral and the Universal Perturbative Invariant of 3-Manifolds

Abstract

The integrality of the Kontsevich integral and perturbative invariants is discussed. We show that the denominator of the degree $n$ part of the Kontsevich integral of any knot or link is a divisor of $(2!3!... n!)^4(n+1)!$. We also show that the denominator of of the degree $n$ part of the universal perturbative invariant of homology 3-spheres is not divisible by any prime greater than $2n+1$.