Complete noncompact Spin(7) manifolds from self-dual Einstein 4–orbifolds

We present an analytic construction of complete non-compact 8-dimensional Ricci-flat manifolds with holonomy Spin(7). The relies on the study adiabatic limit metrics Spin(7) principal Seifert circle bundles over asymptotically conical G2 orbifolds. we produce have asymptotic geometry, so-called ALC that generalises to higher dimensions geometry 4-dimensional ALF hyperk\"ahler metrics. apply our arising from self-dual Einstein 4-orbifolds positive scalar curvature. As illustrative examples power construction, arbitrarily large second Betti number and infinitely many distinct families same smooth 8-manifold.