Spin Holonomy of Einstein Manifolds

Abstract:

Berger's Theorem classifies the linear holonomy groups of irreducible, simply connected Riemannian manifolds. For physical applications, however, it is at least as important to have a classification of the possible spin holonomy groups (defined by the parallel transport of spinors) of non-simply-connected manifolds. We establish a complete classification of the spin holonomy groups of all compact, locally irreducible, Einstein Riemannian spin manifolds of non-negative scalar curvature.