Timeline for Are Banach Manifolds intrinsically interesting?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 15, 2017 at 15:20 | comment | added | Chris Judge | The unit sphere in a Banach space is a Banach manifold. Even if one can realize it as an open subset of the Banach space, it seems more reasonable to think of the sphere as a Banach manifold. Note that Uhlenbeck decisively uses this point of view in her proof that, for example, Laplace eigenvalues are generically simple. | |
| Jul 1, 2014 at 14:46 | comment | added | Deane Yang | A finite-dimensional Banach manifold is called a Finsler manifold and is of interest. | |
| S Jul 1, 2014 at 14:35 | history | suggested | evgeny | CC BY-SA 3.0 |
incorrect ff symbol
|
| Jul 1, 2014 at 14:34 | review | Suggested edits | |||
| S Jul 1, 2014 at 14:35 | |||||
| Dec 4, 2012 at 21:06 | comment | added | Mozibur Ullah | @Evans: you mean infinite-dimensional vector spaces? | |
| Mar 9, 2012 at 14:33 | answer | added | Liviu Nicolaescu | timeline score: 10 | |
| Mar 9, 2012 at 10:24 | answer | added | Georges Elencwajg | timeline score: 26 | |
| Mar 9, 2012 at 7:09 | comment | added | Jonny Evans | Usually the infinite dimensional objects one encounters in geometry are Fréchet manifolds (e.g. diffeomorphism groups or spaces of maps with the smooth topology) and these are really the objects of interest. Banach manifolds are a useful tool for studying infinite dimensions and actually proving anything because there you have the implicit function theorem. In particular if you have an elliptic problem, e.g. holomorphic curves, it's much easier to think of the solution space inside a Banach manifold of maps and then use elliptic regularity it prove it's really inside the smooth locus. | |
| Mar 9, 2012 at 4:02 | comment | added | Mariano Suárez-Álvarez | There is a big difference between the finite-dimentional case and the other: in the latter, manifolds are open subsets of the modeling space, while in the former manifolds rarely are open sets of the modeling space (they embed in a euclidean space of a generally much larger dimension, and even more rarely as open sets thereof) | |
| Mar 9, 2012 at 3:57 | history | asked | Mozibur Ullah | CC BY-SA 3.0 |