The Poincaré conjecture: A problem solved after a century of new ideas and continued work
DOI:
https://doi.org/10.7203/metode.0.9265Keywords:
topología, esfera, grupo fundamental, geometría riemanniana, flujo de Ricci
Abstract
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 proposed by Richard Hamilton.
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Author Biography
María Teresa Lozano Imízcoz, University of Zaragoza (Spain).
References
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Perelman, G. (2003a). Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. ArXiv. Retrieved from https://arxiv.org/abs/math/0307245
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