What is the gentlest notes/book of intro differential topology?
closed as off-topic by Namaste, Xander Henderson, B. Mehta, Tom-Tom, user175968 May 21 '18 at 22:42
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Namaste, Xander Henderson
An Introduction to Manifolds by Loring W. Tu would likely be helpful. It's a textbook written for undergrads, so it works out proofs in detail, but it still covers de Rham cohomology. See Bott and Tu's Differential Forms in Algebraic Topology for a nice sequel when you're done with this one.
As a pretty unconventional suggestion, I would also dare to suggest browsing through Anders Kock's Synthetic Geometry of Manifolds alongside or after reading Tu. Though very different from the usual way of doing differential geometry and topology, it's a great book for getting geometric intuition.
I think a combination of Guillemin & Pollack's Differential Topology and Milnor's Topology from the Differential Viewpoint was what I used. There were pros and cons, but if you have a strongish background in multivariable calculus and analysis this could be good.
I began with Elementary Differential Topology by James R. Munkres. It has the familiarity of Munkres' style and is rather easy to obtain both on the web and in university libraries.