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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.

edited May 8 2010 at 22:05

asked May 8 2010 at 19:50

A Budding Topologist
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	The paper is <a href="resolver.sub.uni-goettingen.de/… 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 2010 at 20:14
	Oh the URLs are automatically linked to without the need for manually adding HTML tags, so here it is again resolver.sub.uni-goettingen.de/… – Thomas Sauvaget May 8 2010 at 20:17

Andy Putman · Accepted Answer · 2010-05-08 20:10:48Z UTC

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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 : http://www.worldscibooks.com/mathematics/6379.html

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?

answered May 8 2010 at 20:10

Andy Putman
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Excellent; many thanks! – A Budding Topologist May 8 2010 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 2010 at 2:03

Sorry, you'd have to ask a real algebraic topologist about that! Equivariant algebraic topology scares me... – Andy Putman May 9 2010 at 2:40

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@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 2010 at 4:36

Thom’s seminal cobordism paper in English?

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