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In Quelques proprietes globales des varietes differentiables, Thom classifies unoriented manifolds up to cobordism. I've been struggling a bit to understand this paper, and while Stong's cobordism notes have helped a bit, I was wondering if an English translation (of the entire paper or just parts) exists. Thank you in advance.

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The paper is <a href="… available from the GDZ project</a> of the University of Goettingen. I don't know if that means it's legal to try and translate the whole paper (for purely academic purposes, any idea?), but at least if only a few words or a few sentences are the problem, then it'd guess it would fall under "fair quotation" or something. – Thomas Sauvaget May 8 '10 at 20:14
Oh the URLs are automatically linked to without the need for manually adding HTML tags, so here it is again – Thomas Sauvaget May 8 '10 at 20:17
up vote 11 down vote accepted

An English translation of this paper is included in the first volume of the "Topological Library", edited by Novikov and Taimanov. See the following website :

By the way, Thom's paper is rather hard to read. There are alternative expositions (often with somewhat easier proofs) of various pieces of it in various places. What portion in particular is giving you trouble?

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Excellent; many thanks! – A Budding Topologist May 8 '10 at 21:21
I can't speak for the OP, but I often want to understand the punchline, or at least have it stated, before going into homotopy theory of uncomfortable-looking spaces. Could you advise where to read about equivariant relative (oriented) bordism, with respect to action of a finite group? (that's what I would like to know everything I can about.) – Daniel Moskovich May 9 '10 at 2:03
Sorry, you'd have to ask a real algebraic topologist about that! Equivariant algebraic topology scares me... – Andy Putman May 9 '10 at 2:40
@Daniel - relatively little is known about oriented equivariant bordism. Even the coefficients of equivariant bordism, especially if one wants to know ring structure, are "wide open" (though I have done some computations in the complex setting). – Dev Sinha May 11 '10 at 4:36

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