References request on characteristic class

Question

I am planing to learn something about characteristic classes on my own. I am wondering if anyone could recommend me something on such materials like constructions of vector bundles, Thom isomorphism theorem with applications and intersection theory. I have a foundation on differential manifolds, riemannian geometry and elmentary algebraic topology, i.e (co)homology groups, kunneth formular, Poincare dualities and so on.

Because I don't have too much time on it, I hope the references could be very readable, concise and ideal for self-studying.

I will appreciate if any one may recommend such references. Thank you.

I don't know if you are still looking into this, but.... I have LaTeXed Milnor's mimeographed notes "Lectures on characteristic classes". It is the precursor of the one mentioned by "anomaly" below. I guess the original notes have still some value, seeing that late Andrew Ranicki has listed them in his online "Library". If you are interested to have a copy, please let me know. — eltonjohn, Jul 04 '21 at 11:01

score 4 · Accepted Answer · answered Apr 13 '15 at 15:46

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The canonical reference is Milnor and Stasheff's "Characteristic Classes." It's definitely readable, concise, and amenable to self-study; my only (very minor) complaint about it is that it's a bit reluctant to stay within the paracompact or CW-complex category. I also like Husemoller's "Fiber Bundles," which covers a bit of topological K-theory as well. If you have a basic background in algebraic topology, you shouldn't have a problem with either book.

answered Apr 13 '15 at 15:46

anomaly

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Hatcher's notes are also nice, even if they don't go into as many topics as M-S. For the more algebraically minded, Bruner-Catanzaro-May have an in-progress book floating around the internet, too. – Apr 13 '15 at 17:36
Thank you for your advice, anomaly. Also thank @MikeMiller for your useful comments. – Jason785 Apr 14 '15 at 14:00
@MikeMiller Do you have a link for that in-progress book? – Sean Tilson Sep 27 '17 at 15:29
@SeanTilson I think I was referring to this. – Sep 27 '17 at 15:30
@MikeMiller Thank you very much! – Sean Tilson Sep 28 '17 at 09:47

References request on characteristic class

1 Answers1