# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 38 (2009) pp.67-81

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### 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.

MSC(Primary) 14J80 57M50 Seiberg-Witten theory, geometric structure, monopole class, parallel spinor.