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PERTURBATIVE INVARIANTS OF LENS SPACES ASSOCIATED WITH COHOMOLOGY CLASSES

CHIFUMI SATO

C4 Technology, Inc. Meguro Tokyu Bldg., 5th Floor, 2-13-17 Kamiosaki Shinagawa-ku, Tokyo 141-0021, Japan

https://doi.org/10.1142/S0218216506004786Cited by:1 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 57M27, 57N10

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