Constructions of compact G2-holonomy manifolds

Abstract

This is a survey paper. We explain the known constructions for two geometrically different classes of examples of compact Riemannian 7-manifolds with holonomy G2. One method uses resolutions of singularities of appropriately chosen 7-dimensional orbifolds, with the help of asymptotically locally Euclidean spaces. Another method uses the gluing of two asymptotically cylindrical pieces and requires a certain matching condition for their cross-sections `at infinity'.

To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"