Timeline for How are infinite-dimensional manifolds most commonly treated?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 9, 2013 at 20:59 | comment | added | Urs Schreiber | Frechet manifolds are probably the most popular, at least in application to mapping spaces (loop groups, etc). But in loads of cases, more useful than the Frechet manifold structure is actually the diffeological space structure. That's really useful, and in many cases this is what is actually being used. One should ask: "In my application, do I absolutely need to know that my space is locally modeled on a vector space?" Most of differential geometry goes through without this extra information. One big exception where one maybe strictly needs local linear structure is integration. | |
| Feb 9, 2013 at 19:36 | comment | added | alvarezpaiva | It seems there are tons of ways to consider infinite-dimensional manifolds. I wonder how many ways are useful (i.e. come naturally in concrete meaningful applications). Could you say a word on this? | |
| Feb 9, 2013 at 18:32 | history | answered | Urs Schreiber | CC BY-SA 3.0 |