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I want to self-study differential topology. I'd like to hear suggestions from you about appropriate books that I could use while studying.

Note: I have not studied differential topology before. I self-studied general topology and some algebraic topology before.

Thank you

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A standard introductory textbook is Differential Topology by Guillemin and Pollack. It was used in my introductory class and I can vouch for its solidity. You might also check out Milnor's Topology from the Differentiable Viewpoint and Morse Theory. (I have not read the first, and I have lightly read the second.)

For other books on topology, Hatcher has a nice list here. You may be interested in books like Bott-Tu or others listed under item III, manifold theory.

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  • $\begingroup$ +1 Thanks for your answer. For the first book that you mentioned, am I missing any of its prerequisites ? $\endgroup$ – Amr Jul 18 '13 at 13:52
  • $\begingroup$ @Amr Have you studied analysis and measure theory, enough to be familiar with Lebesgue integrals? $\endgroup$ – Neal Jul 18 '13 at 13:53
  • $\begingroup$ I did, but I did not go to deep. I studied measure theory from an analysis book. There were 2 chapters on measure theory. I did not study a pure measure theory book. Is this OK ? $\endgroup$ – Amr Jul 18 '13 at 13:55
  • $\begingroup$ I am familiar with lesbesgue integrals as well. $\endgroup$ – Amr Jul 18 '13 at 13:59
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    $\begingroup$ What you need is a multivariable analysis course -- familiarity with the derivative as a linear map, chain rule, inverse/implicit function theorems. You don't need any abstract measure theory, although the notion of measure zero will show up. $\endgroup$ – Ted Shifrin Jul 18 '13 at 14:13

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