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So right now I'm wondering if Munkres Analysis on Manifolds text is sufficient to get a proper foundation for manifolds or would it be better to just bruteforce through Lee's text on Smooth Manifolds? Most of the reviews on Munkres Analysis on Manifolds state that its good but the problems seem to be too easy. So I'm confused if I should stay away from Analysis on Manifolds or just stick with the text.

What would be the best course of action with this dilemma?

Alexander King
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  • It depends on your background, interests and time. But I don't see any harm in reading Lee's awesome book. It also seems that you might be studying manifolds for the first time, so Munkres is a good start, but is indeed not enough, and if you find it very easy, you can jump to another texts (such as Lee). I think the best action is taking lots of books, seeing if you like (and can work through) them, and stick with the ones that suit you most! – EternalBlood Sep 10 '17 at 22:43
  • I forget if Lee's manifolds book covers the point-set topology necessary. There's a few things about topological spaces that are good to know before diving in. If it includes these, you're probably OK to read Lee. – A. Thomas Yerger Sep 10 '17 at 22:53

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