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I am attempting to translate Borel's "Cohomologie de $\text{SL}_{n}$ et valeurs de fonctions zeta aux points entiers" paper into English. Since I know no French, this is a rather crude process heavily involving Google Translate (and also a little common sense). However, I am unable to interpret the phrase "variété à coins". I am led to believe that this translates to something like "wedge variety" or "corner variety". Neither of these terms are familiar to me and a quick Google search turned up nothing, which leads me to my question...

Would someone be kind enough to provide me with an English translation of the phrase "variété à coins"?

For completeness, I include the sentence where the phrase is to be found:-

"Mais en fait la construction précédente fournit une autre démonstration de l’injectivité de $j^{*}_{\Gamma}$; qui, à l’encontre de celle de [4], ne fait pas intervenir la compactification de $X/\Gamma$ en une variété à coins (cf. 5.6)."

The reference for the paper is:-

Borel, Armand. Cohomologie de $\text{SL}_{n}$ et valeurs de fonctions zeta aux points entiers. Ann. Sc. Norm. Super. Pisa 4 (1977) 613-636.

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    $\begingroup$ I think the common english name is "manifold with corner". I'm not sure this question is appropriate for MO, thought... $\endgroup$
    – Adrien
    Commented Jan 8, 2014 at 12:22
  • $\begingroup$ @Adrien Aha, thank you very much. I apologise if this question is not appropriate, and am willing to delete it if that is the done thing? I am curious though; why is this question not suitable for MO? I often see similar translation requests on here. $\endgroup$
    – Oli
    Commented Jan 8, 2014 at 12:39
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    $\begingroup$ Yes. It translates to "manifold with corners". $\endgroup$
    – DamienC
    Commented Jan 8, 2014 at 12:40
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    $\begingroup$ Adrien, I things this questions is perfectly appropriate. It arises in translating a research-level book, and it's a question that only practitioners of the field can answer, so where else? $\endgroup$
    – Joël
    Commented Jan 8, 2014 at 13:48
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    $\begingroup$ I also think this is a fine question. $\endgroup$
    – Andy Putman
    Commented Jan 8, 2014 at 16:38

1 Answer 1

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The translation is "manifold with corners".

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