in the SageManifolds part, most component-wise computations can be performed on multiple cores. However, the wedge product has not been parallelized yet. But since I need this for some computations in "higher" dimensions, I want to contribute this to the project. I had already opened an associated ticket:
https://trac.sagemath.org/ticket/29796. Applying the same approach as for tensor products, I noticed that it results in a slow down even. Furthermore, the number of necessary computations is highly depending on the manifold's dimension and tensor rank of both involved forms. This makes it a little bit difficult to figure out a good parallelization method. On top of that, I have no idea about effective parallelization yet. Thus, I appreciate any help, feedback or tips that I can get.