Complete non-compact G2-manifolds from asymptotically conical Calabi-Yau 3-folds

Understand

We develop a powerful new analytic method to construct complete non-compact G2-manifolds, i.e.

• Riemannian 7-manifolds (M,g) whose holonomy group is the compact exceptional Lie group G2.
• Our construction starts with a complete non-compact asymptotically conical Calabi-Yau 3-fold B and a circle bundle M over B satisfying a necessary topological condition.
• Our method then produces a 1-parameter family of circle-invariant complete G2-metrics on M that collapses to the original Calabi-Yau metric on the base B as the parameter converges to 0.