I have a couple of strong undergraduate students who want to learn differential topology as an independent study with me (they already had a semester of topology). Textbook recommendations? I used Guilleman and Pollack (+ Milnor's book) when I was a student.
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Thank you!
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Oh, of course, Professor Richeson. Thank you for your excellent efforts to convey the substance of serious mathematical ideas to a general readership, for this is crucial work that is, alas, seldom done, and even more seldom done well. We are all in your debt.
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Guillemin & Pollack, as well as Milnor, try to skirt the issue of saying what a manifold is by speaking only of submanifolds of R^n. Seems like a shrewd strategy, and in a sense it "works." But it's wildly ahistorical, and separates the subject from its most natural applications.
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