Timeline for How to "globalize" the inverse function theorem?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 27, 2021 at 12:07 | comment | added | Johnny T. | I was very interested in this result by Hadamard. Do you know if I can take $M$ to be open ball of $\mathbb{R}^n$? I think open ball should be fine, but would a closed ball be fine also? Thank you | |
| Nov 29, 2010 at 4:39 | comment | added | anonymous | Thank you, Andrey and Roy, that's interesting but it's going in a direction which is different from what I originally had in mind. The problem is that, in the notation you adopted, requiring the nonvanishing of Jacobian of $F$ everywhere on $M$ is too restrictive for the applications I need; that's why I used "globalize" (with the quotation marks!) in the title and threw in the remark on sheaves. | |
| Nov 29, 2010 at 0:41 | comment | added | roy smith | Instead of assuming the target simply connected, you might assume the map has degree one in some sense, e.g. some fiber is one point, or if the manifolds are both compact, the map on top homology is isomorphic. | |
| Nov 29, 2010 at 0:28 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
added 22 characters in body
|
| Nov 28, 2010 at 23:27 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
added 294 characters in body
|
| Nov 28, 2010 at 22:49 | history | answered | Andrey Rekalo | CC BY-SA 2.5 |