Exact triangles in monopole homology and the Casson-Walker invariant

Matilde Marcolli; Bai-Ling Wang

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Exact triangles in monopole homology and the Casson-Walker invariant

Matilde Marcolli·Bai-Ling Wang

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Abstract

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.

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BibTeX RIS

Matilde Marcolli, Bai-Ling Wang. 2001-01-16. Exact triangles in monopole homology and the Casson-Walker invariant. https://arxiv.org/abs/math/0101127

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