Talk:Cartan's equivalence method

I need help outsourcing this to other pages as much as possible. Silly rabbit 04:48, 10 November 2005 (UTC)[reply]

As I understand it, the 'method' is in his hands a bit less than algorithmic? It does however have the key idea that the graph of the 'diffeomorphism to construct' is to be constructed by setting up differential forms and thus a differential system for which the graph is a solution manifold (locally ...). Forgive me if this sounds a naive description. As for things on other pages, yes, it is often easier to work on some of the prerequisites first, and then write higher-level pages as hypertext quite dependent on others things. This tends to take a little longer to do than one might expect. On the other hand the alternative is to write pages dense with red links and hope to fill those out later. I don't think there is a single, right way to do it; in the end one has to nduce some sort of 'organic growth' in the coverage here so the top-level contributions don't seem too isolated. Charles Matthews 10:16, 10 November 2005 (UTC)[reply]

You are right, it is less than algorithmic because the process may not always terminate. As for a description of the method, or "algorithm" (although the terminology is not my own), it is hideously complex. Silly rabbit 15:45, 10 November 2005 (UTC)[reply]

I dipped into Cartan's book on his Travaux, which is always interesting if only to try to get the language down. Only half-a-dozen papers on 'equivalence' as such. One of those did sound a bit like early work on CR structures. At the outset it is (in his view) mainly derived from Lie's work, i.e. something like deriving a Lie group action by considering tuples of Pfaffian forms. Which ties up with saying 'coframe fields'. He doesn't really claim novelty for that, though he possibly constructed some of the exceptional Lie groups that way. I also dipped into Chern's Selected Papers, but (although Chern digested as much of it as anyone, AFAICS) the introduction doesn't really offer a general description. Charles Matthews 16:15, 10 November 2005 (UTC)[reply]