The LMO-invariant of 3-manifolds of rank one and the Alexander polynomial |
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Authors: | Jens Lieberum |
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Affiliation: | (1) Mathematical Sciences Research Institute, 1000 Centennial Drive Berkeley, CA 94720-5070, USA (e-mail: lieberum@msri.org), US |
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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 ?rhus invariant of knots. Received February 14, 2000 / Published online October 11, 2000 |
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Keywords: | Mathematics Subject Classification (2000): 57M25 57N65 57M15 |
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