Department Mathematik
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Inhaltsbereich

Mathematical Gauge Theory - WS 2010/2011

Lecturer: Prof. Dr. Martin Schottenloher
Assistent: Christian Paleani

Dates

Lecture:    Mo 12 -14, Room A 027
Lecture:    Tu 14 -16, Room A 027
Tutorial:    Tu 16 -18, Room A 027

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Tutorial

Each week on Tuesday a basic exercise will be assigned. In addition, we prompt the students to invent their own excercises. You should take a problem mentioned e.g. in the lecture, make a concrete problem out of it, explain its importance in detail, solve it, place it into the total context, submit the solution and present it to the other students during the tutorial.
These presentations and the submitted solutions together with the solutions of the weekly assigned exercises will be the foundation of your marks at the end of the course.

Download

  • Manuscripts of selected sections of the course (marked with a #) can be found here: In three formats:
    • ".pdf" universal but big
    • ".djvu" much smaller
    • ".jnt" the windows format in which you can add your own notes.
  • The weekly Exercises.

    Contents

      I. Introduction
      II. Manifolds
    1. The Structure of a Smooth Manifold (# in preparation)
    2. Topology of Manifolds
    3. New Manifolds out of Old Ones (Constructions)
    4. Tangent Vectors
    5. Tangent Space
      III. Vector Fields
    6. Tangent Bundle
    7. Vector Fields #
    8. Flows #
    9. One Forms #
      IV. Tensors and Forms
    10. Multilinear Algebra #
    11. Tensor Fields as Sections #
    12. Differential Forms #
    13. The Hodge Operator
    14. DeRham Cohomology
      V. Fibrations
    15. (Locally Trivial) Fibrations #
    16. Transition Functions #
      VI. Vector Bundles
    17. Vector Bundles #
    18. Operations on Vector Bundles (# in preparation)
    19. Sections
    20. Homotopy and Triviality
    21. Classifying Map #
      VII. Geometry of Vector Bundles
    22. Semi-Riemannian Geometry #
    23. Connections #
    24. The Horizontal Distribution (# in preparation)
    25. Parallel Transport #
    26. Curvature #
    27. Curvature and Structure Equations #
    28. Metric and Orientation #
      VIII. Lie Groups
    29. Lie Groups and Their Lie Algebras #
    30. The Exponential Map #
    31. The Adjoint Representation #
    32. Classical Lie Groups #
      IX. Principal Fibre Bundles
    33. Homogeneous Spaces # + 33B. Homogeneous Spaces: Orbit Space #
    34. The Concept of a Principal Fibre Bundle #
    35. Associated Bundles #
      X. Geometry of Principal Fibre Bundles
    36. The Trivial Case #
    37. Connections on Principal Fibre Bundles #
    38. Associated Connections #
    39. Curvature and Structure Equations #
    40. Gauge Field Theory #
      XI. Characteristic Classes
    41. Weil Homomorphism #
    42. Chern Classes #
    42!

    Links and Sources


    Contact

    Person Emailadresse Sprechstunde
    Prof. Dr. Martin Schottenloher schotten "at" math.lmu.de Mo 14 h
    Christian Paleani cpaleani "at" math.lmu.de