Electromagnetic modeling provides an interesting context to present a link
between physical phenomena and homology and cohomology theories. Over the past
twenty-five years, a considerable effort has been invested by the computational
electromagnetics community to develop fast and general techniques for potential
design. When magneto-quasi-static discrete formulations based on magnetic
scalar potential are employed in problems which involve conductive regions with
holes, \textit{cuts} are needed to make the boundary value problem well
defined. While an intimate connection with homology theory has been quickly
recognized, heuristic definitions of cuts are surprisingly still dominant in
the literature.
The aim of this paper is first to survey several definitions of cuts together
with their shortcomings. Then, cuts are defined as generators of the first
cohomology group over integers of a finite CW-complex. This provably general
definition has also the virtue of providing an automatic, general and efficient
algorithm for the computation of cuts. Some counter-examples show that
heuristic definitions of cuts should be abandoned. The use of cohomology theory
is not an option but the invaluable tool expressly needed to solve this
problem
