Conjecture de poincaré démonstration pdf

Henri poincare posed an epochmaking question, which later came to be termed as poincare conjecture, in one of his papers, which asked. Smooth 4dimensional poincare conjecture open problem garden. Poincare a realise des travaux dimportance majeure en optique et en calcul infinitesimal. However, perelmans work also encompasses a proof of the thurston geometrisation conjecture, a much more signi. Perelmans solution was based on richard hamiltons theory of ricci flow, and made use of results on spaces of metrics due to cheeger, gromov, and perelman himself.

Dec 03, 2006 in this paper, we provide an essentially selfcontained and detailed account of the fundamental works of hamilton and the recent breakthrough of perelman on the ricci flow and their application to the geometrization of threemanifolds. Based on it, we shall give the first written account of a complete proof of the poincare conjecture and the geometrization conjecture of thurston. Pdf in 2002, perelman proved the poincare conjecture, building on the work of richard hamilton on the ricci flow. It should be noted that the piecewise linear or di. Grigory perelman has solved the poincare conjecture. The generalized poincare conjecture is an undergraduatelevel pointset topology problem for. He has shown that, as poincare conjectured, any closed, simply connected 3manifold is homeomorphic to the 3sphere. In fact there is a simple list of all possible smooth compact orientable surfaces. Leur place dans lensemble des mathematiques grandit progressivement. Mar 25, 20 of the seven millenium prize problems, poincare conjecture is the only solved one. John morgan spoke at the icm on the poincare conjecture on august 24, 2006, declaring that in 2003, perelman solved the poincare conjecture. Terence tao perelmans proof of the poincare conjecture.

Introduction it is a great pleasure for me to report on the recent spectacular developments concerning the poincare conjecture. Enonce mathematique quon pense vrai mais quon ne sait pas demontrer. Conjecture, one of the seven milliondollar clay problems, follows from it as a simple corollary. Conjectured by french mathematician henri poincare who, by the way, went through the same university as i did, it was solved by russian mathematician gregori perelman in 2003. By the work of smale and stallings, the topological poincare conjecture was shown to be true provided. The poincare conjecture clay mathematics institute. Gaurav tiwari math understanding poincare conjecture. If a threedimensional shape is simply connected, is it homeomorphic to the threedimensional sphere. Introduction the topology of twodimensional manifolds or surfaces was well understood in the 19th century. Millennium prize for the poincare conjecture to grigoriy perelman. In particular, we give a detailed exposition of a complete proof of the poincare conjecture due to hamilton and perelman. But for milnor and kervaire showed that admits nonstandard smooth structures so the smooth poincare conjecture is false in general. In december 2006, the journal science honored the proof of poincare conjecture as the breakthrough of the year and featured it on its cover. In these papers perelman also proved william thurstons geometrization conjecture, a special case of which is the poincare conjecture.