Timeline for "Practical" references on mapping spaces as infinite-dimensional manifolds
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2022 at 7:37 | comment | added | B.Hueber | @RyanBudney I was reading an article where the authors did things like defining curves in function spaces and taking their derivatives, or defining maps between function spaces and talking about their differential. So, I would like to understand the underlying theory a little bit better, since the authors do not define the structures and definitions around these spaces.... | |
| Dec 1, 2022 at 7:36 | comment | added | B.Hueber | Thanks a lot for the suggestions! | |
| Dec 1, 2022 at 2:29 | comment | added | Ryan Budney | That said, is there a particular reason why you are interested in the smooth structure? | |
| Dec 1, 2022 at 0:27 | comment | added | Ryan Budney | "Introduction to global analysis" by Donald Kahn might be the kind of thing you are looking for? | |
| Nov 30, 2022 at 22:37 | comment | added | Igor Khavkine | If you only care about mapping spaces as Banach manifolds, Lang's classic Differential and Riemannian Manifolds (Springer, 1995) develops basic differential geometry in a way that applies to Banach manifolds. However, he mentions $C^k(M,N)$ spaces specifically only in passing. | |
| Nov 30, 2022 at 21:29 | comment | added | Igor Belegradek | I think you listed all the books on the subject. You may have to learn the language of jet bundles and how to translate to the language of charts. Hirsch does this fairly explicitly in chapter 2, section 4. | |
| Nov 30, 2022 at 21:06 | history | asked | B.Hueber | CC BY-SA 4.0 |