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- Poincaré_duality abstract "In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if M is an n-dimensional oriented closed manifold (compact and without boundary), then the kth cohomology group of M is isomorphic to the (n − k)th homology group of M, for all integers k Poincaré duality holds for any coefficient ring, so long as one has taken an orientation with respect to that coefficient ring; in particular, since every manifold has a unique orientation mod 2, Poincaré duality holds mod 2 without any assumption of orientation.".
- Poincaré_duality wikiPageID "540732".
- Poincaré_duality wikiPageRevisionID "549587835".
- Poincaré_duality subject Category:Duality_theories.
- Poincaré_duality subject Category:Homology_theory.
- Poincaré_duality subject Category:Manifolds.
- Poincaré_duality comment "In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds.".
- Poincaré_duality label "Dualidad de Poincaré".
- Poincaré_duality label "Dualidade de Poincaré".
- Poincaré_duality label "Dualité de Poincaré".
- Poincaré_duality label "Poincaré duality".
- Poincaré_duality label "Poincaré-Dualität".
- Poincaré_duality label "Poincaré-dualiteit".
- Poincaré_duality label "Двойственность Пуанкаре".
- Poincaré_duality label "ポアンカレ双対".
- Poincaré_duality label "龐加萊對偶性".
- Poincaré_duality sameAs Poincar%C3%A9_duality.
- Poincaré_duality sameAs Poincaré-Dualität.
- Poincaré_duality sameAs Dualidad_de_Poincaré.
- Poincaré_duality sameAs Dualité_de_Poincaré.
- Poincaré_duality sameAs ポアンカレ双対.
- Poincaré_duality sameAs 푸앵카레_쌍대성.
- Poincaré_duality sameAs Poincaré-dualiteit.
- Poincaré_duality sameAs Dualidade_de_Poincaré.
- Poincaré_duality sameAs Q2063099.
- Poincaré_duality sameAs Q2063099.
- Poincaré_duality wasDerivedFrom Poincaré_duality?oldid=549587835.