Poincaré conjecture: A problem solved after a century of new ideas and continued work


Abstract


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


Keywords


mathematics; millennium problems; Poincaré conjecture; Henri Poincaré

References


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