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

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

1997-04-25

arxiv.org/abs/q-alg/9704017v1

Mathematics

Geometric Topology

27 pages, LaTeX with graphics package

Scientific paper

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 $2n+1$.

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