Anti-self-duality of curvature and degeneration of metrics with special holonomy (Q1781830)

The authors study the structure of non-collapsed Gromov-Hausdorff limits of sequences, \(M_i^n\), of Riemannian manifolds with special holonomy. They prove that these spaces are smooth manifolds with special holonomy off a closed subset of codimension \(\geq 4\). If, in addition, the manifolds are compact and the sequence of certain characteristic numbers, \(C(M_i)\), is bounded, the authors obtain detailed information about the singular set. These results support the authors' conjecture that off a closed subset of codimension at least \(6\), the singularities are of orbifold type and the orbifold structure is compatible with the holonomy group.