Comment by WhyOhWhyQ
3 days ago
It's truly the best book on Smooth Manifolds, though if you'd like a gentler approach which is still useful, then I suggest Loring Tu's books. Lee's Topological Manifolds book is also very nice. His newest edition of the Riemannian manifolds book requires selective reading or it'll slow you down.
What's the relation between the different Lee manifolds? Is it a sequence you're supposed to read in order?
Lee taught Intro to Topological Manifolds for one quarter, and then the next two quarters where Intro to Smooth Manifolds. Then Riemannian, then vector bundles, and then complex manifolds.
That's a great suggestion. I actually started with Topological Manifolds before moving on to Introduction to Smooth Manifolds and it really helped build a solid foundation.
I havent read Loring Tus books before but let me look at them since I have been wanting to revisit the topic with a clearer and more relaxed approach.