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

2000/02/05 by Lieberum, Jens
#57M15 #57M25 #57N65 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.math/0002040

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.

Related

• The Alexander polynomial and finite type 3-manifold invariants
• Homology handles with trivial Alexander polynomial
• The L²-Alexander torsion of 3-manifolds
• L²-Alexander invariant for knots
• The Alexander polynomial of (1,1)-knots