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Basic question: are there (co)homological or sheaf-based tools which might be useful in geometric measure theory? Background: The jumping off point here is a simple analogy - geometric measure ...

Let $M$ be a smooth manifold. Let $Z\subset M$ be a smooth submanifold which is a closed subset. Let $F$ denote the sheaf of generalized functions (equivalently, Schwartz distributions) on $M$, namely ...