Poincaré duality
Poincaré duality also reverses dimensions; it corresponds to the fact that, if a topological manifold is represented as a cell complex, then the dual of the complex (a higher-dimensional generalization of the planar graph dual) represents the same manifold. In Poincaré duality, this homeomorphism is reflected in an isomorphism of the "k"th homology group and the ("n" − "k")th cohomology group.