Math 518: Differentiable Manifolds I

Basic Information


Point set topology and linear algebra.
If you have any questions or concerns, please contact me by e-mail.

Course outline

  1. 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; vector bundles; manifolds with boundary; orientations.

  2. 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, DeRham cohomology.

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The course grade will be based on weekly homework (35%), a midterm (25%) and a final (40%).

Last modified: Fri March 20 15:06:06 CST 2015