Narrow Results

The quantum SO(3)-invariants of ℚ-homology 3-spheres can be perturbatively expanded to the Ohtsuki invariant in number theory. On the other hand, it is known that the quantum SU(2)-invariants of 3-manifolds M admits a refinement involving a mod 2 cohomology class of M. A motivation of this paper is to study whether a perturbative expansion can be derived from the refinement. In this paper, we shall prove to be able to derive the perturbative expansion in the case of lens spaces by a concrete calculation, and shall define the perturbative invariant. Furthermore we obtain some properties for the perturbative invariant for covering spaces and connected sums of lens spaces.