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Categories: Homology theory Manifolds Duality theories Surgery theory |
Summary Of: Poincaré dualityA form of Poincaré duality was first stated... Poincaré duality did not take on its modern form until the advent of cohomology in the 1930s... and formulated Poincaré duality in these new terms... Poincaré duality was classically thought of in terms of dual... The modern statement of the Poincaré duality theorem is in terms of homology and cohomology... so Poincaré duality in particular implies that the homology and cohomology groups of orientable closed... This approach to Poincaré duality was used by Przytycki and Yasuhara to give an elementary homotopy and diffeomorphism classification of... is a version of Poincaré duality which provides an isomorphism between the homology of an abelian covering space of a manifold... precisely so as to generalise Poincaré duality to such stratified spaces...Encyclodia Page On: Poincaré duality |
