I'm sorry for such a basic question, but I can't seem to find this term defined anywhere. I'm trying to learn analysis on manifolds, and google has not been any help in figuring out what this thing is. I know what a differential form is, what a volume form is, but I can't figure this one out for some reason.
2026-03-31 18:03:06.1774980186
What is a top form?
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On a $n$-dimensional Manifold $M$ all differential $k-$forms with $k > n$ are zero. This just comes from the fact that the $k-$th exterior powers of a $n-$dimensional vector space are trivial if $k > n$. Therefore you can only have (nontrivial) $k-$forms if $k \leq n$. So the maximal possible (i.e. top!) degree is $n$, hence these forms are called top-degree, top-dimensional or just top forms.