I have been intrested lately in a simplicial version of Stokes theorem, which intuitively I think should be true in simplicial settings.
I think if $X$ is a simplicial complex and $X(k)$ are its $k$-cells, I think something along the lines of
$$ \int_\Omega d\alpha =\int_{d\Omega} \alpha ,$$
should be true, where $\alpha$ is an anti-symmetric map $\alpha:X(k)\to \mathbb{F}$ and $d$ is the co-boundary map, and $\mathbb{F}$ is an appropriate field. I have so far been unsucsessful in finding such a result and was wondering whether someone has found an appropriate result.
I have however found this thread on the website which refers to this result. But this seems to be adressing co-homology in a way which I am not sure is equivalent to how I described as anti-symmetric maps from $k$-cells. Also the other issue is that I am not sure whether this result is indeed valid, since I am myself not that comfortable with co-homology.
I will give some further context and say that I am interested in such result to give bounds on norms of elements of the form $d\alpha$.
I would appreciate any helpful remarks regarding any step of the points I've asked about.