In an n dimensional space if you have a p-form the Hodge star operation maps this form onto an n-p dimensional form.

If this seems familiar then it is, in Stokes' Theorem you take the form over a certain space (the form being the integral element, the space being the surface of the object under consideration) and you map it to (i.e. identify it with) a form of associated with the volume. (bad explaination, sorry, anyone else?)

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