Timeline for Understanding exterior differential systems
Current License: CC BY-SA 4.0
6 events
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| Jul 27 at 13:26 | comment | added | Bilateral | Thanks a lot. It is quite fascinating that these powerful results were known so long ago. Discussing nowadays with some mathematicians it seems that the power of the techniques of EDS is not so well-known and is considered to be a "hard topic". I was wondering if the cohomological techniques you developed in "Characteristic Cohomology of Differential Systems (I): General Theory" are relevant to the EDS of my question, namely if there is any non-trivial cohomology associated with it. | |
| Jul 25 at 9:01 | comment | added | Robert Bryant | @Bilateral: If you look at the final section of those notes, you'll see several applications of Theorem 4. I don't know any other place where Theorem 4 is stated explicitly in the form that I gave in those notes, but I confess that I don't know the EDS literature of the 1930-40s that well. Because the proof of Theorem 4 via Cartan-Kähler is so straightforward, I believe that some version of Theorem 4 was known to Élie Cartan (and I'm sure that he would have regarded it as 'obvious' after Kähler's extension of Cartan's existence theorem to differential ideals generated in arbitrary degree). | |
| Jul 22 at 20:04 | comment | added | Bilateral | Thanks a lot! I am studying your review "Notes on exterior differential systems" and now I understand that I am precisely in the situation that you describe on page 17. In particular, Theorem 4 in that review is very useful for me. Since there are no citations there, I don't know if this is new material or if it can be found elsewhere. Do you know of any references where that particular situation is further explored? | |
| Jul 22 at 19:59 | vote | accept | Bilateral | ||
| Jul 19 at 17:01 | history | edited | Robert Bryant | CC BY-SA 4.0 |
Fixed some typos and cleaned up a few badly worded sentences.
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| Jul 19 at 15:37 | history | answered | Robert Bryant | CC BY-SA 4.0 |