The second paragraph of this gives a quick definition of pseudocycle. It is then shown that the group of pseudocycle equivalences and the Z homology are isomorphic as graded abelian groups. The pseudocycle groups can be readily endowed with a product. Show that it is isomorphic to the usual homology intersection product, preferably in the context of non-compact manifolds and BM homology. If you are interested in doing this project, please find someone else in the class to join you and discuss this with me. Depending on where you currently are in your graduate studies, this may be a great use of your time or not so great.