I am teaching a introductory course on differentiable manifolds next term. The course is aimed at 4th fourth year US undergraduate students and 1sts first year US graduate students who have done basic coursework in point-set topology and multivariable calculus, but may not know the definition of differentiable manifold. I am following the textbook Differential Topology by Guillemin and Pollack, supplemented by Milnor's book.
My question is: what What are good topics to cover that are not in assigned textbooks?
