Prof. D. Kotschick: Mathematical Gauge Theory

(The course covers the module WP 16 (Mathematical Gauge Theory I) for the TMP program in theoretical and mathematical physics, and is worth 9 ECTS points.)

• Place and Time: Tue, Wed 10-12, Room B 132
  
• Exercise class: Wed 2-4 PM , Room B 132
  The Scheine can be collected in the Prüfungsamt starting on July 22, 2008.
• Syllabus: This is a course on the geometry and topology of fibre bundles, covering in particular the following topics:
  Lie groups and Lie algebras; fibre bundles with structure groups; principal and associated bundles; connections and curvature; gauge transformations; Chern-Weil theory of characteristic classes; gauge-invariant functionals on spaces of connections.
  
• Notes: Here is a short explanation of the smooth manifold structure of a homogeneous space G/H, due to P. Eberlein.
• Audience: Students of mathematics and/or physics (third year and above).
  
• Prerequisites: Basics of smooth manifolds; the contents of Differential Geometry I is more than sufficient.


• References: 1. For background, and for the first chapter on Lie groups, Lie algebras, and integrability theorems:
  L. Conlon: Differentiable Manifolds, Birkhäuser Verlag
  F. W. Warner: Foundations of Differentiable Manifolds and Lie Groups, Springer Verlag
  2. For the main part of the course:
  K. Nomizu: Lie Groups and Differential Geometry, Mathematical Society of Japan
  D. Bleecker: Gauge Theory and Variational Principles, Addison Wesley
  S. Kobayashi and K. Nomizu: Foundations of Differential Geometry I, John Wiley and Sons