A note on the index bundle over the moduli space of monopoles

Abstract

Donaldson has shown that the moduli space of monopoles Mk is diffeomorphic to the space Ratk of based rational maps from the two-sphere to itself. We use this diffeomorphism to give an explicit description of the bundle on Ratk obtained by pushing out the index bundle from Mk. This gives an alternative and more explicit proof of some earlier results of Cohen and Jones. © 1995 Springer-Verlag.