THE LMO-INVARIANT OF 3-MANIFOLDS OF RANK ONE AND THE ALEXANDER POLYNOMIAL

JENS LIEBERUM

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 Århus invariant of knots.