Geometry & Topology 14 (2010) 1993–2045

DOI: 10.2140/gt.2010.14.1993

Abstract

It is known that perturbative invariants of rational homology 3–spheres can be constructed by using arithmetic perturbative expansion of quantum invariants of them. However, we could not make arithmetic perturbative expansion of quantum invariants for 3–manifolds with positive Betti numbers by the same method.

In this paper, we explain how to make arithmetic perturbative expansion of quantum SO(3) invariants of 3–manifolds with the first Betti number 1. Further, motivated by this expansion, we construct perturbative invariants of such 3–manifolds. We show some properties of the perturbative invariants, which imply that their coefficients are independent invariants.

Keywords

3–manifold, quantum invariant, perturbative invariant

Mathematical Subject Classification

Primary: 57M27

References

Publication

Received: 28 August 2009
Revised: 27 May 2010
Accepted: 7 July 2010
Published: 29 August 2010
Proposed: Vaughan Jones
Seconded: Joan Birman, Shigeyuki Morita.

Authors