2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60761We 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 figuresGeometric Topology57R58, 57R57, 57M27text