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The Poincaré conjeture : a problem solved after a century of new ideas and continued

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The Poincaré conjeture : a problem solved after a century of new ideas and continued

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Lozano Imízcoz, María Teresa
Aquest document és un/a article, creat/da en: 2018

The Poincaré conjecture is a topological problem established in 1904 by the French mathematician Henri Poincaré. It characterises three-dimensional spheres in a very simple way. It uses only the first invariant of algebraic topology ? the fundamental group ? which was also defined and studied by Poincaré. The conjecture implies that if a space does not have essential holes, then it is a sphere. This problem was directly solved between 2002 and 2003 by Grigori Perelman, and as a consequence of his demonstration of the Thurston geometrisation conjecture, which culminated in the path pro-posed by Richard Hamilton.
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