Monopoles on Sasakian Three-folds

We consider monopoles with singularities of Dirac type on quasiregular Sasakian three-folds fibering over a compact Riemann surface $Σ$, for example the Hopf fibration $S^3\longrightarrow S^2$. We show that these correspond to holomorphic objects on $Σ$, which we call twisted bundle triples. These are somewhat similar to Murray's bundle gerbes. A spectral curve construction allows us to classify these structures, and, conjecturally, monopoles.

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