Geometry & Topology
- Geom. Topol.
- Volume 6, Number 1 (2002), 27-58.
Torsion, TQFT, and Seiberg–Witten invariants of $3$–manifolds
We prove a conjecture of Hutchings and Lee relating the Seiberg–Witten invariants of a closed 3–manifold with 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 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 . 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 in the case that is a mapping torus.
Geom. Topol., Volume 6, Number 1 (2002), 27-58.
Received: 16 October 2001
Accepted: 25 January 2002
First available in Project Euclid: 21 December 2017
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Mark, Thomas E. Torsion, TQFT, and Seiberg–Witten invariants of $3$–manifolds. Geom. Topol. 6 (2002), no. 1, 27--58. doi:10.2140/gt.2002.6.27. https://projecteuclid.org/euclid.gt/1513882788