Talk:De Rham cohomology

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Ok, what we have here in technical terms is called a mess. The Hodge decomposition ought to be exported to Hodge theory, although I'm not quite sure how to do that -- especially since de Rham is already discussed in detail there. Furthermore, Hodge's theorem on elliptic operators is not actually necessary to prove the de Rham theorem (despite the fact that it is a very elegant application of this theorem). There are many simpler techniques which do not rely on Sobolev spaces and other kludges (such as the Eilenberg-Steenrod axioms). So the options are, really clarify how the Hodge decomposition applies to this theorem (at the end of the article), or find a way to incorporate this material into some other article (preferably without making anyone angry). Silly rabbit

[edit] de Rhan's theorem

since the statement of de Rhan's theorem requires a compact manifold, perhaps an example of a non-compact manifold where the theorem fails would enrich this entry.