Relative topological integrals and relative Cheeger-Simons differential characters

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. © 2002 Elsevier Science B.V. All rights reserved.