Title: Torsion, TQFT, and Seiberg–Witten invariants of 3–manifolds
Abstract: We prove a conjecture of Hutchings and Lee relating the Seiberg-Witten invariants of a closed 3-manifold X with b 1 ≥ 1 to an invariant that "counts" gradient flow lines-including closed orbits-of a circle-valued Morse function on the manifold.The proof is based on a method described by Donaldson for computing the Seiberg-Witten invariants of 3-manifolds by making use of a "topological quantum field theory," which makes the calculation completely explicit.We also realize a version of the Seiberg-Witten invariant of X as the intersection number of a pair of totally real submanifolds of a product of vortex moduli spaces on a Riemann surface constructed from geometric data on X .The analogy with recent work of Ozsváth and Szabó suggests a generalization of a conjecture of Salamon, who has proposed a model for the Seiberg-Witten-Floer homology of X in the case that X is a mapping torus.