Asymptotic Geometry of G_2 monopoles
G_2 monopoles are special solutions of the Yang-Mills-Higgs equation on G_2 manifolds, and Donaldson and Segal conjectures that one can construct invariants of noncompact G_2 manifolds by counting G_2 monopoles.
One of the first steps of achieving this goal is understanding the analytic behavior of these monopoles. In this talk, I introduce the proper analytic setup for the problem, and present our results about the asymptotic form of G_2 monopoles on Asymptotically Conical manifolds with structure group being SU(2).
If time permits, I also talk about our further plans in this project, in particular:
1. Generalizations of these results to manifolds with fibered end and higher rank gauge groups.
2. A glue-in construction of monopoles with ``large mass''.
This is a join project with Goncalo Oliveira (UFF, Brazil).