  Topological integrals appear frequently in Lagrangian field theories. On
manifolds without boundary, they can be treated in the framework of (absolute)
(co)homology using the formalism of Cheeger--Simons differential characters.
String and D--brane theory involve field theoretic models on worldvolumes with
boundary. On manifolds with boundary, the proper treatment of topological
integrals requires a generalization of the usual differential topological set
up and leads naturally to relative (co)homology and relative Cheeger--Simons
differential characters. In this paper, we present a construction of relative
Cheeger--Simons differential characters which is computable in principle and
which contains the ordinary Cheeger--Simons differential characters as a
particular case.
