  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:
Ch^k(X,dX) x Ch^{n-k-1}(X) --> S^1, given by (a,b) l-->(a*b)[X], induces
isomorphisms:
  D : Ch^k(X,dX) --> Hom^{smooth}(Ch^{n-k-1}(X), S^1)
  D': Ch^{n-k-1}(X) --> Hom^{smooth}(Ch^k(X, dX), S^1) onto the smooth
Pontrjagin duals. In particular, D and D' 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,dX). The relation of the sequence to the duality mappings is
analyzed.

Differential Geometry;Algebraic Topology