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 |
News
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
- The Structure of a Smooth Manifold (# in preparation)
- Topology of Manifolds
- New Manifolds out of Old Ones (Constructions)
- Tangent Vectors
- Tangent Space
III. Vector Fields - Tangent Bundle
- Vector Fields #
- Flows #
- One Forms #
IV. Tensors and Forms - Multilinear Algebra #
- Tensor Fields as Sections #
- Differential Forms #
- The Hodge Operator
- DeRham Cohomology
V. Fibrations - (Locally Trivial) Fibrations #
- Transition Functions #
VI. Vector Bundles - Vector Bundles #
- Operations on Vector Bundles (# in preparation)
- Sections
- Homotopy and Triviality
- Classifying Map #
VII. Geometry of Vector Bundles - Semi-Riemannian Geometry #
- Connections #
- The Horizontal Distribution (# in preparation)
- Parallel Transport #
- Curvature #
- Curvature and Structure Equations #
- Metric and Orientation #
VIII. Lie Groups - Lie Groups and Their Lie Algebras #
- The Exponential Map #
- The Adjoint Representation #
- Classical Lie Groups #
IX. Principal Fibre Bundles - Homogeneous Spaces # + 33B. Homogeneous Spaces: Orbit Space #
- The Concept of a Principal Fibre Bundle #
- Associated Bundles #
X. Geometry of Principal Fibre Bundles - The Trivial Case #
- Connections on Principal Fibre Bundles #
- Associated Connections #
- Curvature and Structure Equations #
- Gauge Field Theory #
XI. Characteristic Classes - Weil Homomorphism #
- Chern Classes #
II. Manifolds
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