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How should I call briefly the space $M$, which is obtained when "forgetting" the origin (i.e. the identity) of an $n$-dimensional torus $T$ (i.e. $T$ is a compact $n$-dimensional abelian Lie group)?

I found the expression "$M$ is the principal homogeneous space (or torsor) over $T$" (see http://en.wikipedia.org/wiki/Principal_homogeneous_space, which explains also what I mean precisley by forgetting the origin).

But I find this expression a bit too sophisticated (I think not every mathematician knows what a torsor is) for such a simple and probably very common object. Isn't it?

When $T$ is substituted by a vector space, I would of course say "$M$ is an affine space" (instead of "prinicipal homogeneous space over a vector space").

Is there also in the case of a torus such a standard name which is more likely to be immediately understood?

After my searching on google it seems not the case, which I find bit curious.

(I found a few papers using "compact affine space", but it seems to me they mean somthing else).

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