Abstract
The moduli space of the solutions to the monopole equations over an oriented closed 3-manifold M carrying the geometric structure $\mathbf{R} \times H^2$ is studied. Solving the parallel spinor equation, we obtain an explicit solution to the monopole equations. The moduli space consists of a single point with the Seiberg-Witten invariant $\pm 1$. Further, the (anti-)canonical line bundle $K_M^\pm 1$ gives a monopole class of M.
Citation
Mitsuhiro ITOH. Takahisa YAMASE. "Seiberg-Witten theory and the geometric structure $\mathbf{R} \times H^2$." Hokkaido Math. J. 38 (1) 67 - 81, February 2009. https://doi.org/10.14492/hokmj/1248787012
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