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What happens to a closed manifold to ensure it is homeomorphic to a torus $T^{n}$
If $M$ is a smooth connected closed $n$-dimensional manifold, its universal covering space is homeomorphic to Euclidean space $R^{n}$, and its fundamental group is $Z^{n}$, then is it homeomorphic to a torus $T^{n}$? If not, why?
