Gauss’s Law and Residue Calculus in the Framework of Cohomology Theory

A. In this paper, our aim is to incorporateGauss’s famous law in electrodynamics and some of Cauchy’s results in residue calculus within the general setting of deRham cohomology, that will be shown to provide amost natural environment for their development. Namely, it will be demonstrated that forms defined and closed on punctured spaces can be assigned a residue similar to the one defined in complex analysis. This can be achieved in any number of dimensions and is, in essence, an extension of Gauss’s three dimensional law: monopole fields generate the deRham cohomology groups of those spaces andwith their helpwewill outline a method for evaluating certain kinds of multiple improper integrals.