Exact triangles in monopole homology and the Casson-Walker invariant

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We establish the exact triangle in Seiberg-Witten-Floer theory relating the monopoloe homologies of any two closed 3-manifolds which are obtained from each other by $\pm 1$-surgery. We also show that the sum of the modified version of the Seiberg-Witten invariants for any closed rational homology 3-sphere $Y$ over all $Spin^c$ structures equals to $\frac 12 |H_1(Y, \Z)| λ(Y)$ where $λ(Y)$ is the Casson-Walker invariant.
35 pages, 3 figures

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Geometric Topology, 57R58, 57R57, 57M27

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http://salesiana.dossiersoluciones.com/handle/123456789/60761

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0101127
 http://arxiv.org/abs/math/0101127

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arXiv