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.



What does "variété à coins" translate to in English?
The translation is "manifold with corners".


