Poincaré Conjecture
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High Quality Content by WIKIPEDIA articles! In mathematics, the Poincaré conjecture (French, pronounced [pw ka e]) is a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds. It began as a popular, important conjecture, but is now considered a theorem to the satisfaction of the awarders of the Fields medal. The claim concerns a space that locally looks like ordinary three dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, the Poincaré conjecture (French, pronounced [pw ka e]) is a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds. It began as a popular, important conjecture, but is now considered a theorem to the satisfaction of the awarders of the Fields medal. The claim concerns a space that locally looks like ordinary three dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is just a three-dimensional sphere. An analogous result has been known in higher dimensions for some time.