Math 543 Geometry and Manifold Theory I: Complex Manifolds

Spring 2005

The course will meet MWF 3-4 in 199 Cupples I. The first class is Wednesday, January 19.

I'll be covering most of Shiing-Shen Chern's book "Complex Manifolds without Potential Theory", Second Edition, Springer-Verlag, New York 1979, ISBN 0-387-90422-0. I've asked the Campus Bookstore to order copies of this book.

A list of topics:
1. Complex manifolds, examples.
2. Complex and Hermitian structures on a vector space.
3. Almost complex manifolds, integrability conditions.
4. Sheaves and cohomology.
5. Complex Vector bundles, connections.
6. Holomorphic vector bundles and line bundles.
7. Hermitian geometry and Kaehlerian geometry.
8. Characteristic classes.

Prerequisites: Math 441 and Math 421 (or the equivalent of an introductory complex variables course like Math 416). No prior knowledge of sheaf theory, vector bundles or connections in vector bundles will be assumed.

Homework will be assigned and corrected in some way, possibly by presentations in regularly scheduled homework presentation sessions, possibly by a grader. The purpose of the homework will be to give students assistance in learning the material.
There will be no examinations.


Gary Jensen
Last modified: Wed Jan 12 11:51:41 CST 2005