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A non-abelian Seiberg-Witten invariant for integral homology 3-spheres. (English) Zbl 1065.57031
The author introduces quaternionic Seiberg-Witten equations on the spinor bundle coupled with the SU(2) bundle on an integral homology three sphere. To define the Seiberg-Witten invariant, he uses a novel perturbation which is not associated with the Chern-Simons-Dirac functional hence not suitable for the Seiberg-Witten-Floer homology. The invariant is independent of the orientation of the three-manifold and its linear combination with the SU(3)-Casson invariant of Boden-Herald gives a \({\mathbb Z}\) mod \(4{\mathbb Z}\) invariant for unoriented integral homology 3-spheres.

MSC:
57R57 Applications of global analysis to structures on manifolds
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
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