Instantons from Bows

Bows generalize quivers, forming the first step of the sequence: quiver, bow, sling, monowall. 

Kronheimer and Nakajima discovered how quivers organize the data encoding all Yang-Mills instantons on Asymptotically Locally Euclidean spaces.  Bows, in turn, organize data encoding instantons on Asymptotically Locally Flat (ALF) spaces.  We shall describe the bow construction of instantons and how any instanton on an ALF space gives rise to a bow representation.  

We begin with the estimates generalizing Uhlenbeck’s theorem to ALF setting and establis the index theorem.  Then we compute the topological classes of any instantons in terms of the bow representation.  These are results of the current work with Mark Stern and Andres Larrain-Hubach.