@ThomasKlimpel, finished separate paper about these rotational invariants: arxiv.org/pdf/1801.01058
It is from perspective of machine learning application, offers much more than standard e.g. spherical harmonics ... also there are systematic ways to generate large number of invarians (fig. 2), which should finally handle graph isomorphism - I will try it in a week or two
@JoshuaHerman, these are just rotation invariants for polynomials - using algebraic varieties for manifold learning, these invariants would allow you to test differing by rotation ... regarding homology groups, they are already rotation invariant
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