Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Friday, April 01, 2011 - 16:00 in V3-204

Holonomy groups: classification, constructions, and applications

A talk in the 'Oberseminar Eichtheorie und Topologie' series by
Thomas Leistner from Adelaide
Abstract: The holonomy group of a semi-Riemannian manifold is defined as the group of parallel transports along loops at a point in the manifold. The holonomy group measures how curved a manifold is and thus becomes an important tool when studying parallel objects and geometric differential equations on the manifold. This lecture gives an overview about recent results about the classification and construction of holonomy groups of semi-Riemannian manifolds. We will start by introducing holonomy groups and their basic properties, describe the classification problem and its solution for Riemannian manifolds. Then we will focus on own results including the classification of holonomy groups of Lorentzian manifolds, applications to spinor fields equations using metric cones, and some construction methods for manifolds of special holonomy.

Within the CRC this talk is associated to the project(s): C1