Timeline for Gluing two diffeomorphisms together
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1 at 17:37 | history | edited | Piotr Hajlasz |
edited tags
|
|
| Mar 27 at 21:22 | answer | added | Piotr Hajlasz | timeline score: 4 | |
| Jan 29, 2023 at 18:47 | comment | added | Piotr Hajlasz | Did you get a satisfactory answer to your question? I have been struggling with exactly the same problem that you asked. I asked a question mathoverflow.net/q/439635/121665 which when you think about it is more or less a reformulation of your problem: when you have a smooth diffeomorphism of a sphere it is almost linear at infinity when you take a stereographic projection. I stated it in the way I did because of connection to well known problems in topology. | |
| Sep 16, 2010 at 3:08 | vote | accept | Vaughn Climenhaga | ||
| Sep 12, 2010 at 22:15 | comment | added | Vaughn Climenhaga | @Mariano and @Tom: Ah, right... duly noted. Thanks for pointing that out -- I've edited the question accordingly. (I realise that by doing so I've removed some of the context for your comments, so I'm not sure if this is best practice or not. If it's not, I'm happy to undo the edits and let the comments tell the story.) | |
| Sep 12, 2010 at 22:13 | history | edited | Vaughn Climenhaga | CC BY-SA 2.5 |
Changed question slightly in light of comments
|
| Sep 12, 2010 at 19:01 | answer | added | Bill Thurston | timeline score: 12 | |
| Sep 12, 2010 at 19:01 | comment | added | Tom Goodwillie | You can even make examples such that $f$ has no continuous extension to the closed ball. So maybe revise the question: Either assume that $f$ is given on a closed ball, or else leave the hypothesis alone but only demand that $F$ should agree with $f$ on a smaller ball, not on the whole domain. | |
| Sep 12, 2010 at 18:42 | comment | added | Mariano Suárez-Álvarez | (For example: there is a diffeo mapping the unit disc $D$ in $\mathbb R^2$ to the unit disc minus one of its radii. | |
| Sep 12, 2010 at 18:38 | comment | added | Mariano Suárez-Álvarez | By "folding" $B(\delta)$ you can construct $f$ satisfying your conditions for which no continuous extension to $\overline{B(\delta)}$ is injective. | |
| Sep 12, 2010 at 18:36 | comment | added | Vaughn Climenhaga | I've added a more to-the-point statement of what I'm after -- hopefully that clears it up a bit. | |
| Sep 12, 2010 at 18:36 | history | edited | Vaughn Climenhaga | CC BY-SA 2.5 |
Clarified question
|
| Sep 12, 2010 at 18:30 | comment | added | Mariano Suárez-Álvarez | What is exactly your question? | |
| Sep 12, 2010 at 18:15 | history | asked | Vaughn Climenhaga | CC BY-SA 2.5 |