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I’ve recently read about Clifford’s geometric algebra being a more general framework for differential geometry than differential forms, simpler for the study of spaces with a metric tensor, and equivalent to the latter in some cases.

I’ve mostly learned about differential forms in the context of de Rham cohomology so I couldn’t help but asking myself if there’s an equivalent concept in the framework of Clifford algebras (I don’t know a whole lot about Clifford algebras yet so excuse me if this question doesn’t make sense).

dahemar
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    In $\mathbb R^n$, I think up to sign, $\mathrm d$ is basically the same as what someone working with Clifford algebra might write as $\vec\nabla\wedge$. So I would imagine you could get the same basic de Rahm cohomology story in a slightly different language. But I don't have experience with actually doing this so can't write a full answer. – Mark S. Aug 01 '21 at 14:57

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