Explore: Conjecture De Poincaré

In the mathematical field of geometric topology, the Poincaré conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about

Poincaré conjecture), Fermat's Last Theorem, and others. Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf

Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the Millennium Meeting held on May 24, 2000. Thus, on the official

More specifically, the conjecture states that certain de Rham cohomology classes are algebraic; that is, they are sums of Poincaré duals of the homology

problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. Poincaré is regarded

theorem Poincaré algebra K-Poincaré algebra Super-Poincaré algebra Poincaré–Bjerknes circulation theorem Poincaré complex Poincaré conjecture, one of

the Poincaré conjecture, was solved by Grigori Perelman in 2003. However, a generalization called the smooth four-dimensional Poincaré conjecture—that

mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to

The Poincaré Conjecture – Proved". Science. 314 (5807): 1848–1849. doi:10.1126/science.314.5807.1848. PMID 17185565. "The Poincaré Conjecture". Archived

|\leq q^{d/2}} Poincaré duality then implies that | α | = q d / 2 . {\displaystyle |\alpha |=q^{d/2}.} This proves the Weil conjectures for the middle