Abstract

An ALC (asymptotically locally conical) manifold is a complete non-compact Riemannian manifold whose ends are modelled on circle fibrations over Riemannian cones of one lower dimension with fibres of asymptotically constant finite length. In dimension 4 and when the asymptotic cone is flat the acronym ALF (asymptotically locally flat) is more commonly used. (Conjectural) examples of ALC manifolds with G2 holonomy have appeared both in the physics and mathematics literature since the early 2000’s. ALC G2 manifolds provide interesting models for understanding how compact G2 manifolds can collapse to Calabi-Yau 3-folds. In this talk I will discuss the construction of various families of ALC G2 manifolds and describe their geometric properties. This is joint work with Mark Haskins (Imperial College London) and Johannes Nordström (University of Bath).