Abstract.
The integrality of the Kontsevich integral and perturbative invariants is discussed. It is shown 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 prove this by establishing the existence of a Drinfeld's associator in the space of chord diagrams with special denominators. We also show that the denominator 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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Oblatum 20-VI-1997 & 28-IV-1998 / Published online: 12 November 1998
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Le, T. On denominators of the Kontsevich integral and the universal perturbative invariant of 3-manifolds. Invent math 135, 689–722 (1999). https://doi.org/10.1007/s002220050298
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DOI: https://doi.org/10.1007/s002220050298