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

TL;DR

This paper uses a diffeomorphism between monopole moduli spaces and rational maps to explicitly describe the index bundle, providing a clearer proof of previous results.

Contribution

It offers an explicit description of the index bundle over rational maps, simplifying earlier proofs of related topological properties.

Findings

Explicit description of the index bundle over $ ext{Rat}_k$

Alternative proof of Cohen and Jones's results

Enhanced understanding of the topology of monopole moduli spaces

Abstract

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