The talk’s main aim is to present and discuss two fundamental results in differential geometry and algebraic topology: the “Poincare Duality” theorem and the “Thom Isomorphism” theorem.
Firstly, we will recall what the homology groups of a topological manifold are and how the cap product is defined. Secondly we plan to state the theorems and sketch their proofs, at least in the easy cases. Finally, we will see some natural applications of these results in various contexts.