Basic Information

• Instructor: Eugene Lerman
• e-mail: lerman at math dot uiuc dot edu
• Homepage: http://www.math.uiuc.edu/~lerman
• Course page: http://www.math.uiuc.edu/~lerman/520/520syl.html
• Office: 336 Illini Hall
• Office Hours: TBA and by appointment.
• Phone: 244-9510
• Class meets: MWF 10 am    in 343 Altgeld Hall

Prerequisites

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; Whitney Embedding Theorem; 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.
   
   
3. Other topics: Sard's Theorem, Distributions and the Frobenius Theorem; intersection theory and degree; Lefschetz Fixed Point Theorem; Poincare-Hopf Index Theorem; DeRham cohomology.

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Grades