Book
I will not use a textbook. Below are some references, a few of which can be downloaded free of charge through the links provided if you are affiliated with Cornell. A very detailed exposition of most of the topics covered in the course can be found in [L].
- [AMR]
- R. Abraham, J. Marsden, and T. Ratiu, Manifolds, tensor analysis, and applications, second edition, Applied Mathematical Sciences 75, Springer-Verlag, New York, 1988. Springer link.
- [B]
- N. Bourbaki, Variétés différentielles et analytiques, Éléments de mathématique, Fascicule de résultats, Springer-Verlag, 2006. Springer link.
- [GP]
- V. Guillemin and A. Pollack, Differential topology, AMS Chelsea Publishing, 2010. AMS link.
- [H]
- M. Hirsch, Differential topology, Graduate Texts in Mathematics 33, Springer-Verlag, New York, 1994. Springer link.
- [L]
- John M. Lee, Introduction to Smooth Manifolds, second edition, Graduate Texts in Mathematics 218, Springer-Verlag, 2012. Springer link.
- [M]
- John W. Milnor, Topology from the differentiable viewpoint, second corrected printing, University Press of Virginia, 1969.