ON DENOMINATORS OF THE KONTSEVICH INTEGRAL AND

THE UNIVERSAL PERTURBATIVE INVARIANT OF 3-MANIFOLDS

THANG T. Q. LE

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.