Ben Smith, McGill University
“Singular G-Monopoles on circle bundles over a Riemann surface”
This talk will outline the essential ingredients involved in the functorial correspondence between irreducible singular G-monopoles on S1 × Σ and ⃗t-stable meromorphic bundles on Σ. The main theorem here is thus a generalization of a recent article by B. Charbonneau and J.C. Hurtubise from unitary to arbitrary compact, reductive gauge groups. The required distinctions and similarities for unitary versus reductive gauge are outlined and many parallels are drawn for easy transition. Some basic theory involving induced connections on associated bundles is developed for the purpose of differentiating G-equivariant maps between principal bundles.
Once the main correspondence theorem is understood, the spectral data of our monopoles is provided and the groundwork for a monopole theory on Sasakian manifolds, along with their analogous abelianization is discussed.