On the set of the logarithm of the LMO invariant for integral homology 3-spheres

Abstract

AbstractThe LMO invariant is a very strong invariant such that it is expected to classify integral homology 3-spheres. In this paper we identify the set of the degree ≤ 6 parts of the logarithm of the LMO invariant for integral homology 3-spheres. As an application, we obtain a complete set of relations which characterize the set of Ohtsuki's invariants {λi(M)} fori≤ 6. For any simple Lie algebra$\frak{g}$, we also obtain a complete set of relations which characterize the set of perturbativeP$\frak{g}$invariants {$\lambda^{\frakg}_i$(M)} fori≤ 3.