Torsion invariants of Spinᶜ-structures on 3-manifolds

Recently there has been a surge of interest in the Seiberg-Witten invariants of 3-manifolds, see [3], [4], [7]. The Seiberg-Witten invariant of a closed oriented 3-manifold M is a function SW from the set of Spin c-structures on M to Z. This function is defined under the assumption b1(M) ≥ 1 where b1(M) is the