![]() ![]() By developing a number of new techniques and results in the theory of Ricci flow, Grigori Perelman was able to modify and complete Hamilton's program. ![]() Hamilton's program of using the Ricci flow to attempt to solve the problem. Attempts to resolve the conjecture drove much progress in the field of geometric topology during the 20th century. Poincaré hypothesized that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere. Originally conjectured by Henri Poincaré in 1904, the theorem concerns spaces that locally look like ordinary three-dimensional space but which are finite in extent. In mathematical field of geometric topology, the Poincaré conjecture ( UK: / ˈ p w æ̃ k ær eɪ/, US: / ˌ p w æ̃ k ɑː ˈ r eɪ/, French: ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
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