SoSe 2017 - Differential Geometry 2

The lecture course  Differential Geometry 2 will (at least initially) follow the book "Gauge Theory and Variational Principles" by D. Bleecker. The topics covered will include
  +  Differential forms
  +  Lie groups and Lie algebras
  +  Principal fibre bundles
  +  Vector bundles
  +  Connections and curvature
  +  Characteristic classes

     The physical applications in gauge theory will be used as illustration and motivation if wanted, but the main focus is on the mathematical concepts that can be seen as a generalisation of those studied in Differential Geometry 1. There, a fundamental invariant of a Riemannian manifold was its curvature, but to define this is not straightforward and relies on the concept of a connection. In Differential Geometry 2 this will be revised and extended in a more conceptual way, helping to understand even the special case of the Levi-Civita connection better.
     The topics are fairly standard and hence covered in many textbooks. A small selection of possible sources can be found below.

Reading List Differential Geometry

David Bleecker: "Gauge Theory and Variational Principles"
Helga Baum: "Eichfeldtheorie"
Ilka Agricola, Thomas Friedrich: "Globale Analysis"
Klaus Jänich: "Vektoranalysis"

Time Table