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I'm searching for a freely available text that introduces topological and smooth manifolds. I don't need much, just their basic properties and a bit more motivation than the wikipedia articles offers. Maybe course notes of some course that covered them.

(Background: I skipped the classes where topological manifolds were introduced, and now I can't solve any problem where they appear, and I would like to change this before the exam ;)

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2 Answers 2

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I am very sure these links will be very useful.

http://www.dpmms.cam.ac.uk/~agk22/mfds.pdf

http://www.math.toronto.edu/mgualt/MAT1300/week1.pdf

http://www.math.washington.edu/~lee/Books/Smooth/c01.pdf

http://www.math.sunysb.edu/~azinger/mat531-spr10/lect1to5.pdf

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  • $\begingroup$ @Benno. For good book, I will recommend Geometry of Differential Forms (Translations of Mathematical Monographs) by Shigeyuki Morita. $\endgroup$
    – smanoos
    Jan 5, 2012 at 22:59
  • $\begingroup$ Thanks, I'll look for it in our library. $\endgroup$
    – Benno
    Jan 6, 2012 at 12:26
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Lee's books are great. There is also a very nice book by Tu called An Introduction to Manifolds which is relatively new.

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    $\begingroup$ These books are not "freely available". $\endgroup$
    – epimorphic
    Jun 1, 2015 at 21:41

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