I'm an undergraduate who visited a course on differential manifolds and now I have the task to reformulate the maxwell equations in terms of differential forms. The most obvious question that arises first is: On what manifold are the forms defined?
Unfortunately, it seems to be difficult to get good answers. Some people say Minkowski space is just the $\mathbb R^4$, others completely ignore this point. I know that there are a lot of related questions, but the answers are either not satisfactory (especially for a mathematician studying differential geometry) or contain too advanced maths for an undergraduate.
I assume that it is not easy (or even impossible) to give a definite answer, but I'd like to hear some opinions on this. If you know of a reference where this is discussed in more detail, please let me know.