Course textbooks
For Math 8302, there is one "official" course textbook:
- Introduction to smooth manifolds, by John M. Lee.
This textbook, however, should be viewed as supplemental to the lectures. There will be a nontrivial amount of material covered that does not come from this text, and our definitions will not be exactly the same. Moreover, it is often beneficial to get several perspectives on the same material. The lectures themselves will be much closer to the following references.
- Topology from the differentiable viewpoint, by John Milnor. This is a relatively concise (and highly influential) set of notes on differential topology.
- Differential topology, by Guillemin and Pollack. This is a larger textbook which is very much in the same spirit as Milnor's notes.