Is there a way to do calculations with tensors on arbitrary smooth manifolds without fixing a dimension and/or a coordinate system? (things like tensor products, contractions, covariant derivatives, Lie derivatives, exterior calculus, Riemann Tesnsor, torsion tensor,...)

The physcis package (thougfh really good otherwise)  always needs a dimension and a metric, default being 4 dimesnion and Minkowski, metric "arbitrary" is not an option since dimension must still be fixed and calculations become extremely slow and cluttered for very low dimesnional manifolds.

The DifferentialGeometry seems to always need a fixed dimension and a coordinate system. Or am I overlooking some options? 

I would need a solution for either using only geometric objects or an abstract index notation a la Wald (ideally without assuming holonomic bases). 

The only external package I could find is tensorpack, but this seems to be no longer maintained and depends on other packages (Riemann, Canon) which seem to be no longer maintained as well, and it has some drawbacks, e.g. consistent handling of dummy indices is not enforced (e.g. renaming when a conflict arises)

Is there any solution?