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.
A basic course in topology or real analysis.
Instructor's notes, and Differential Topology by Guillemin and Pollack.
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 will be assigned each Friday and will be due the following Friday.
The grade is based on class participation (the students are expected to attend all lectures), and homework assignments.