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: Mon, Thu 10-12, Room B 046
  
• Exercise class: Mon 4-6 PM , Room B 006
  
• Syllabus: This is a course on the geometry and topology of fibre bundles, covering in particular the following topics:
  Lie groups and Lie algebras; principal and associated bundles; connections and curvature; gauge transformations; Chern-Weil theory of characteristic classes; gauge-invariant functionals on spaces of connections.
  
• Lecture notes
• Other 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 Differentiable Manifolds 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
  C. H. Taubes: Differential Geometry: Bundles, Connections, Metrics and Curvature, Oxford University Press
  D. Bleecker: Gauge Theory and Variational Principles, Addison Wesley
  S. Kobayashi and K. Nomizu: Foundations of Differential Geometry I, John Wiley and Sons