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

Yuhan Lim
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Abstract

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.

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Yuhan Lim. 2004-11-01. Defining an SU(3)-Casson/U(2)-Seiberg-Witten integer invariant for integral homology 3-spheres. https://arxiv.org/abs/math/0411024

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