Book
I will not use a textbook. Below are some references, a few of which can be downloaded free of charge through the Springer 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].
- [A]
- R. Abraham, J. Marsden, and T. Ratiu, Manifolds, tensor analysis, and applications, second edition, Applied Mathematical Sciences 75, Springer-Verlag, New York, 1988.
- [B]
- N. Bourbaki, Variétés différentielles et analytiques, Éléments de mathématique, Fascicule de résultats, Springer-Verlag, 2006. Réimpression inchangée des éditions de 1967 et de 1971. Springer link.
- [H]
- M. Hirsch, Differential topology, corrected reprint of 1976 edition, Graduate Texts in Mathematics 33, Springer-Verlag, New York, 1994.
- [L]
- John M. Lee, Introduction to Smooth Manifolds, Second Edition, Graduate Texts in Mathematics 218, Springer-Verlag, 2012. Springer link.