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Aug 30, 2012 at 21:15 comment added J. GE Misha, thanks for the clarification.
Aug 30, 2012 at 21:11 comment added Misha GB: Igor meant "non-isometric"; however, your question, I think, was about flat manifolds regarded as topological manifolds.
Aug 30, 2012 at 21:08 comment added J. GE What did you mean "uncountably many flat tori"?
Aug 30, 2012 at 13:20 history answered Igor Rivin CC BY-SA 3.0