(where is the th homology group of with integer coefficients and the th cohomology (http://planetmath.org/DeRhamCohomology) group) for all , which is given by cap product with a generator of (a choice of a generator here corresponds to an orientation). This isomorphism exists with coefficients in regardless of orientation.
This isomorphism gives a nice interpretation to cup product. If are transverse submanifolds of , then is also a submanifold. All of these submanifolds represent homology classes of in the appropriate dimensions, and
where is cup product, and in intersection, not cap product.
|Date of creation||2013-03-22 13:11:36|
|Last modified on||2013-03-22 13:11:36|
|Last modified by||mathcam (2727)|