Math 520: Differentiable Manifolds I
- Instructor: Eugene Lerman
- e-mail: lerman at math dot uiuc dot edu
- Course page:
- Office: 336 Illini Hall
- Office Hours: TBA and by appointment.
- Phone: 244-9510
- Class meets: MWF 10 am in 343
Prerequisites Point set topology and linear algebra will be very
If you have any questions or concerns, please contact me by e-mail.
- Manifolds: Definitions and examples including projective spaces and
Lie groups; smooth functions and mappings; submanifolds; Inverse Function
Theorem and its applications including transversality; (co)tangent vectors
and bundles; Whitney Embedding Theorem; manifolds with boundary;
- Calculus on Manifolds: Vector fields, flows, and Lie
derivative/bracket; differential forms and the exterior algebra of forms;
orientations again; exterior derivative, contraction, and Lie derivative
of forms; integration and Stokes Theorem.
- Other topics: Sard's Theorem,
Distributions and the Frobenius Theorem; intersection
theory and degree; Lefschetz Fixed Point Theorem; Poincare-Hopf Index
Theorem; DeRham cohomology.
Text An Introduction to Differential Manifolds (Paperback) by Dennis Barden and Charles B. Thomas, Imperial College Press; Reprint edition (March 2003).
course grade will be based on weekly homework (35%),
a midterm (25%) and a final (40%).
lecture of 11/16: Mayer-Vietoris
Last modified: Mon Nov 26 15:06:06 CST 2007