Seiberg-Witten-Floer homology of a surface times a circle for non-torsion spin\(^{\mathbb C}\) structures. (English) Zbl 1082.57025
The authors study the Seiberg-Witten-Floer homology groups of the 3-manifold \(\Sigma\times S^1\), where \(\Sigma\) is a surface of genus \(g\). They compute the Seiberg-Witten-Floer groups of these manifolds, and give a complete determination of their ring structure, for any \(\text{Spin}^{\mathbf C}\) structure with non-vanishing first Chern class.
This study is motivated by considerations of closed 4-manifolds, as the computation of these groups is a necessary ingredient in the description of the Seiberg-Witten invariants for a closed 4-manifold obtained as a normal connected sum along surfaces with self-intersection number zero. The authors give applications to computing Seiberg-Witten invariants in this setting. In the final section, they give a different proof of the higher type adjunction inequalities obtained by P. Oszváth and Z. Szabó [J. Differ. Geom. 55, 385–440 (2000; Zbl 1028.57031)].
This study is motivated by considerations of closed 4-manifolds, as the computation of these groups is a necessary ingredient in the description of the Seiberg-Witten invariants for a closed 4-manifold obtained as a normal connected sum along surfaces with self-intersection number zero. The authors give applications to computing Seiberg-Witten invariants in this setting. In the final section, they give a different proof of the higher type adjunction inequalities obtained by P. Oszváth and Z. Szabó [J. Differ. Geom. 55, 385–440 (2000; Zbl 1028.57031)].
Reviewer: Terry Fuller (Northridge)
MSC:
| 57R57 | Applications of global analysis to structures on manifolds |
| 57N13 | Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) |
Citations:
Zbl 1028.57031References:
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