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How is the two dimensional torus $T^2$, different than a torus? I'm supposed to construct a universal cover of $T^2$ as part of an assignment but I just want to make sure I'm working on the right problem. My guess is that there is no difference and $T^2=S^1\times S^1$ which is just the normal torus we're used to.

Bob
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    What are your definitions of "two dimensional torus $T^2$" and "a torus"? –  Feb 26 '16 at 08:35
  • I guess that you are seeing mathematical descriptions of these objects, it would help to know what they are. – Lee Mosher Feb 26 '16 at 13:53
  • The problem just asks, "Find the universal cover of $T^2$, the two dimensional torus." That task isn't two hard at all now that I know that it's just the normal torus. – Bob Feb 26 '16 at 16:36

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Yes, $T^2=S^1\times S^1$ is what is often just called a "torus". More generally, an "$n$-dimensional torus" is a product $T^n=(S^1)^n$ of $n$ copies of $S^1$.

Eric Wofsey
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