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I have been reading through the wikipedia article about Chern classes and it currently has a section devoted to the Alexander Grothendieck axiomatic approach. The language used throughout the section ("He shows using the Leray-Hirsch theorem (...)") seems to imply that there is a paper or a book written by Grothendieck himself containing the results mentioned.

Thus, my question is: does such a paper exist? Did Grothendieck ever write about the topological Chern classes?

I started my search by reading through a paper referenced in the wikipedia article, La théorie des classes de Chern and it very well may be what I am looking for. I can't tell, because, being written in french, it is basically unreadable to me. Still, I have a feeling that this is not the right paper, because it doesn't reference the aforementioned Leray-Hirsch theorem and the notation used throughout highly suggests that this is the algebro-geometrical case.

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I think this is the right paper. As you suspect, Grothendieck writes it in the language of algebraic vector bundles over algebraic varieties, but he notes at the beginning of the text that it applies just as well to topological manifolds and yields Chern classes for non-singular complex analytic varieties. "On notera que l'exposé donné ici vaut dans d'autres cadres..." – Martin Jan 7 '13 at 15:02
would you like to read the section on hatcher? – Bombyx mori Jan 11 '13 at 11:23
What section on Hatcher? – Piotr Pstrągowski Jan 11 '13 at 17:46
The section user32240 mentions (which by the way is 3.1 of Hatchers Book on Vector bundles and K-Theory) is pretty classical and worth reading, but it is not exactly Grothendiecks approach. – Ben Jan 15 '13 at 14:10

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