Math 519: Differentiable Manifolds II
Basic Information
- Instructor: Professor Eugene Lerman
- e-mail: lerman at math uiuc edu
- Homepage:
http://www.math.uiuc.edu/~lerman
- Course page:
http://www.math.uiuc.edu/~lerman/519/s12/s12.html
- Office: 336 Illini Hall
- Office Hours:
see my calendar
- Phone: 244-9510
- Class meets: MWF 11-11:50 in
343 Altgeld Hall
Prerequisites
I presume you know the material in math 518.
If you have any questions or concerns, please contact me by e-mail.
Grade
The course grade will be based on homework and class
participation.
Course outline
- de Rham cohomology (partially a review)
- Degree (review), linking numbers
- Principal bundles and the associated bundles
- Connections and curvature on vector bundles and principal bundles
- Characteristic classes
Text
Recommended texts (there is no required text):
- Differential Forms in Algebraic Topology by Raoul
Bott and Loring Tu.
- Geometry of Differential Forms
by Shigyuki Morita
- Deformation Quantization and
Index Theory by Boris Fedosov (first 30-35 pages)
- Lectures on Seiberg-Witten Invariants by John D. Moore,
available through
Springerlink
At the beginning of the course the following notes
by Victor Guillemin may be useful. (These form the last bit of this
course).
See this link for homework assignments
and more course related materials
Last modified: Tue Jan 17 12:51:02 CST 2012