  We prove homological stability for two different flavours of asymptotic
monopole moduli spaces, namely moduli spaces of framed Dirac monopoles and
moduli spaces of ideal monopoles. The former are Gibbons-Manton torus bundles
over configuration spaces whereas the latter are obtained from them by
replacing each circle factor of the fibre with a monopole moduli space by the
Borel construction. They form boundary hypersurfaces in a partial
compactification of the classical monopole moduli spaces. Our results follow
from a general homological stability result for configuration spaces equipped
with non-local data.
