Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds

Understand

We present an analytic construction of complete non-compact 8-dimensional Ricci-flat manifolds with holonomy Spin(7).

• The construction relies on the study of the adiabatic limit of metrics with holonomy Spin(7) on principal Seifert circle bundles over asymptotically conical G2 orbifolds.
• The metrics we produce have an asymptotic geometry, so-called ALC geometry, that generalises to higher dimensions the geometry of 4-dimensional ALF hyperk\"ahler metrics.
• We apply our construction to asymptotically conical G2 metrics arising from self-dual Einstein 4-orbifolds with positive scalar curvature.