Math 572b, Differential Geometry, Winter 2004

This course will be an introduction to manifolds and differential geometry, starting right from the beginning. The topics are chosen to be of interest in both mathematics and physics, and the material will be presented in a way that is accessible to students with different backgrounds.

Course outline: manifolds, vector fields, differential forms, de Rham cohomology, bundles, connections, curvature, Riemannian and Lorentzian metrics, geodesics. We will briefly indicate the connections to Yang-Mills theory, gauge theory and general relativity.

Text: I will use "Gauge Fields, Knots and Gravity" by John Baez and Javier Muniain as well as "Differentiable Manifolds" (second edition) by Lawrence Conlon. Both will be on reserve at the Taylor library. I am placing orders for both books, so let me know if you want me to get one or both for you. Here is a list of supplementary texts you may like to refer to.

Presentations: In the second half of the semester, each student will give one presentation on a topic related to the course. The scheduling will be worked out later.

Evaluation: Homework will be due roughly every two weeks. Evaluation will be based upon homework and the presentations. There will be no tests.

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