Solution of the Poincaré conjecture - Wikipedia, the free encyclopedia
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This entry describes the solution of the Poincaré conjecture at a level intended for the general public. The proof described is that of Grigori Perelman using the Ricci flow developed by Richard Ham...
en.wikipedia.org/wiki/Solution_of_the_Poincaré_conjectu...
en.wikipedia.org/wiki/Solution_of_the_Poincaré_conjecture
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A widely accessible statement of the Poincaré Conjecture and its implications, with various links and references for further inquiry.
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mathworld.wolfram.com/PoincareConjecture.html
mathworld.wolfram.com/PoincareConjecture.html
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If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. ... On the other hand, if we imagine that the same rubber band has somehow been stretched in Poincaré, almost a hundred years ago,
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www.claymath.org/millennium/Poincare_Conjecture/
www.claymath.org/millennium/Poincare_Conjecture/
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There has been a great deal of research surrounding the Poincare Conjecture since I first wrote this page many years ago. Most recently, Grisha Perelman has announced a proof of it; in fact, he has announced a proof of the far more sweeping Geometrization Conjecture.
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www.math.unl.edu/~mbrittenham2/ldt/poincare.html
www.math.unl.edu/~mbrittenham2/ldt/poincare.html
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Poincaré‘s conjecture says that no matter what it looks like, it’s a sphere. The conjecture gives mathematicians a short and easy way to identify a deformed blob as a sphere in disguise. ... In its original form, however, the Poincaré conjecture concerned three-dimensional spheres (i.e., 3-spheres).
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seedmagazine.com/content/article/what_is_the_poincare_c...
seedmagazine.com/content/article/what_is_the_poincare_conjecture/
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One of the great stories of mathematics in recent years has been the proof of the Poincare conjecture by Grisha Perelman. This has been one of the most famous open problems in mathematics and has been around for about one hundred years.
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www.math.columbia.edu/~woit/wordpress/archives/000077.h...
www.math.columbia.edu/~woit/wordpress/archives/000077.html
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Actually, the reason the Poincare conjecture is hard to prove is not that high dimensions are hard to visualize. The Poincare conjecture was first proved by Smale for manifolds of dimension 4 or more. Later Freedman was able to prove the 4-dimensional case, which is much harder.
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scienceblogs.com/goodmath/2006/08/the_poincar_conjectur...
scienceblogs.com/goodmath/2006/08/the_poincar_conjecture.php
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There's an interesting article in the Times today about Grisha Perelman and the Poincare conjecture: ... Poincare conjecture? OK, imagine you've drawn a circle on the surface of a balloon. Now imagine slowly distorting the balloon so that the circle shrinks to a point. You can always do that with a 3-dimensional balloon.
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scienceblogs.com/principles/2006/08/the_poincare_conjec...
scienceblogs.com/principles/2006/08/the_poincare_conjecture.php
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