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About: Poincaré complex     Goto   Sponge   NotDistinct   Permalink

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Type: yago:Abstraction100002137yago:Cognition100023271yago:Explanation105793000yago:HigherCognitiveProcess105770664yago:Process105701363yago:PsychologicalFeature100023100programming languageyago:Theory105989479yago:Thinking105770926yago:WikicatDualityTheories New Facet based on Instances of this Class

In mathematics, and especially topology, a Poincaré complex (named after the mathematician Henri Poincaré) is an abstraction of the singular chain complex of a closed, orientable manifold. The singular homology and cohomology groups of a closed, orientable manifold are related by Poincaré duality. Poincaré duality is an isomorphism between homology and cohomology groups. A chain complex is called a Poincaré complex if its homology groups and cohomology groups have the abstract properties of Poincaré duality.