Exact triangles in monopole homology and the Casson-Walker invariant

Details Exact triangles in monopole homology and the Casson-Walker invariant Exact triangles in monopole homology and the Casson-Walker invariant

2001-01-16

arxiv.org/abs/math/0101127v1

Mathematics

Geometric Topology

35 pages, 3 figures

Scientific paper

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 $\frac 12 |H_1(Y, \Z)| \lambda (Y)$ where $\lambda (Y)$ is the Casson-Walker invariant.

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