Cauchy residues and de Rham homology (Q753214)

This article gives an excellent exposition of the author's approach to \(de\quad Rham\) homology. The duality with \(de\quad Rham\) cohomology comes out easily and isomorphisms with smooth singular and singular homology are obtained via the Mayer-Vietoris sequence. After introducing relative homology and the local orientation class from this point of view, a generalization of the classical Cauchy residue theorem is obtained from Stokes' theorem.