A non-abelian Seiberg-Witten invariant for integral homology 3-spheres (Q1428391)

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.