Defining an SU(3)-Casson/U(2)-Seiberg-Witten integer invariant for integral homology 3-spheres

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The SU(3)-Casson invariant for integral homology 3-spheres as studied by Boden-Herald possesses a 'spectral flow obstruction' to being an integer valued invariant which depends only on the non-degenerate (perturbed) moduli space of flat SU(3)-connections. This obstruction is the non-trivial spectral flow of a family of twisted signature operators in 3-dimensions. The parallel U(2)-Seiberg-Witten construction also has an obstruction but from the non-trivial spectral flow of a family of twisted Dirac operators. By taking the SU(3)-flat and U(2)-Seiberg-Witten equations simultaneously the obstructions can be made to cancel and an integer invariant is obtained.
51pp

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Differential Geometry, Geometric Topology, 57R57

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http://salesiana.dossiersoluciones.com/handle/123456789/73066

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411024
 http://arxiv.org/abs/math/0411024

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arXiv