  Some moduli spaces of irregular connections on the trivial bundle over the
Riemann sphere will be identified with Nakajima quiver varieties. In particular
this enables us to associate a Kac-Moody root system to such connections
(yielding many isomorphisms between such moduli spaces, via the reflection
functors for the corresponding Weyl group). The possibility of 'reading' a
quiver in different ways also yields numerous isomorphisms between such moduli
spaces, often between spaces of connections on different rank bundles and with
different polar divisors. Finally some results of Crawley-Boevey on the
existence of stable connections will be extended to this more general context.
