We present an analytic construction of complete noncompact
–dimensional Ricci-flat
manifolds with holonomy
.
The construction relies on the study of the adiabatic limit of metrics with holonomy
on principal Seifert circle bundles over asymptotically conical
–orbifolds.
The metrics we produce have an asymptotic geometry, so-called ALC
geometry, that generalises to higher dimensions the geometry of
–dimensional
ALF hyperkähler metrics.
We apply our construction to asymptotically conical
–metrics arising from
self-dual Einstein
–orbifolds
with positive scalar curvature. As illustrative examples of the
power of our construction, we produce complete noncompact
–manifolds
with arbitrarily large second Betti number and infinitely many distinct families of ALC
–metrics on the same
smooth
–manifold.
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