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Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?

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It is not useful directly, but the method of Ricci flow was originally developed in Physics as the approximate renormalization group flow of the nonlinear 2d sigma model, and so the methods are directly related to string physics. –  Ron Maimon Jun 19 '12 at 21:07
    
A particular application: arxiv.org/abs/1204.0278 –  Willie Wong Jan 25 '13 at 12:59
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