Poincaré duality [SEP] named after
Poincaré duality
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 "k"th cohomology group of "M" is isomorphic to the (formula_1)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
Chow group
In algebraic geometry, the Chow groups (named after Wei-Liang Chow by ) of an algebraic variety over any field are algebro-geometric analogs of the homology of a topological space. The elements of the Chow group are formed out of subvarieties (so-called algebraic cycles) in a similar way to how simplicial or cellular homology groups are formed out of subcomplexes. When the variety is smooth, the Chow groups can be interpreted as cohomology groups (compare Poincaré duality) and have a multiplication called the