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.
"Complete noncompact Spin(7) manifolds from self-dual Einstein $4$–orbifolds." Geom. Topol. 25 (1) 339 - 408, 2021. https://doi.org/10.2140/gt.2021.25.339