Lefschetz-Pontrjagin duality for differential characters

A theory of differential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paper is the formulation and proof of a Lefschetz-Pontrjagin Duality Theorem, which asserts that the pairing given by (alpha, beta) (alpha * beta) [X] induces isomorphisms onto the smooth Pontrjagin duals. In particular, and are injective with dense range in the group of all continuous homomorphisms into the circle. A coboundary map is introduced which yields a long sequence for the character groups associated to the pair (X, X). The relation of the sequence to the duality mappings is analyzed.