Introduction to differential manifolds and smooth maps between them. Topics covered include tangent bundles, differential map,
regular values, Morse functions, transversality, degree theory,
tensors and forms, integration on manifolds, Stokes theorem and de Rham cohomology.
Prerequisites
A basic course in topology or real analysis.
Textbooks
Instructor's notes, and Differential Topology by Guillemin and Pollack.
Auxilary Reading
Various topics in the class also appear in Topology from Differentiable View Point and Morse Theory, by John Milnor; Calculus on Manifolds by Spivak. For more advanced topics or further study, see Stable Mappings and Their Singularities by Gollubitsky and Guillemin, and Introduction to the h-Principle by Eliashberg and Mishachev.
Homework
Homework will be assigned most Wednesdays and will be due the following Wednesday. The assignments will be announced on Canvas, and are to be turned in on Canvas.
Grading
The grade is based on class participation (the students are expected to attend all lectures), homework assignments (15%),
a Midterm (35%) on Wednesday October 4th, and a Final exam (50%) on Friday, Dec 8, 11:20 AM - 2:10 PM.