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The LMO-invariant of 3-manifolds of rank one and the Alexander polynomial

Jens Lieberum
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Abstract

We prove that the LMO-invariant of a 3-manifold of rank one is determined by the Alexander polynomial of the manifold, and conversely, that the Alexander polynomial is determined by the LMO-invariant. Furthermore, we show that the Alexander polynomial of a null-homologous knot in a rational homology 3-sphere can be obtained by composing the weight system of the Alexander polynomial with the Aarhus invariant of knots.

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Jens Lieberum. 2000-02-16. The LMO-invariant of 3-manifolds of rank one and the Alexander polynomial. https://arxiv.org/abs/math/0002040

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