Timeline for Extending a diffeomorphism of the sphere $S^2$ to the ball $D^3$
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 14, 2022 at 10:44 | comment | added | Sam Nead | Igor, Ryan - This has now been done by Balmer and Kleiner - arxiv.org/abs/1909.08710 | |
| Mar 14, 2022 at 10:37 | history | edited | Sam Nead | CC BY-SA 4.0 |
typesetting
|
| Mar 14, 2022 at 10:31 | history | edited | Sam Nead | CC BY-SA 4.0 |
typesetting
|
| Dec 13, 2011 at 19:03 | vote | accept | Daniel Moskovich | ||
| Nov 23, 2011 at 14:29 | comment | added | Ryan Budney | @Igor: Ian Agol has a blog post about this. The surgeries one has to do seems very much in spirit with Allen's original approach to the problem, so it's not clear to me there's a significant gain, at least in using such a straight-up approach. | |
| Nov 15, 2011 at 10:23 | comment | added | Igor Rivin | I would not be surprised if Perelmanian techniques could be adapted to give a proof of this... (But I am sure others have thought of this). | |
| Nov 14, 2011 at 6:47 | comment | added | Chris Gerig | @Scott: Allen*. | |
| Nov 14, 2011 at 2:24 | answer | added | Ryan Budney | timeline score: 9 | |
| Nov 14, 2011 at 2:06 | comment | added | Ryan Budney | @Igor: there's a few but not many. @Scott: I think Allen is well aware it's not an easy read, so this is not news. I think several people are trying to find alternative proofs, or to at least to simplify Hatcher's proof. There are quite a few theorems in the realm of diffeomorphism groups of manifolds that could use cleaning-up and rewriting, not just this theorem of Hatcher's. IMO it's about time to compile them all and put them in one place. | |
| Nov 14, 2011 at 1:40 | answer | added | Tom Goodwillie | timeline score: 26 | |
| Nov 14, 2011 at 0:45 | comment | added | Scott Carter | I wonder when Alan is going to respond to that comment :) | |
| Nov 13, 2011 at 23:03 | comment | added | Igor Rivin | A propos @Tom's comment, I have never met anyone who admitted to having read and understood Hatcher's paper, so a simpler proof is very much called for. | |
| Nov 13, 2011 at 23:02 | answer | added | Igor Rivin | timeline score: 9 | |
| Nov 13, 2011 at 22:18 | comment | added | Tom Goodwillie | The statement that the space of orientation-preserving diffeomorphisms of $S^n$ is connected can easily be manipulated into various equivalent statements, for example: the space of compactly supported diffeomorphisms of $\mathbb R^n$ is connected. In the case $n=2$ it can be proved using either complex analysis or the Poincare-Bendixson Theorem about flows of vector fields in the plane. The $n=1$ case is trivial by comparison. After (re)proving the $n=2$ case, Smale conjectured the $n=3$ case, and it was proved much later by Hatcher. The statement is false for most values of $n$. | |
| Nov 13, 2011 at 22:02 | answer | added | Andy Putman | timeline score: 15 | |
| Nov 13, 2011 at 22:00 | history | edited | Daniel Moskovich | CC BY-SA 3.0 |
4th question added; typo corrected; deleted 8 characters in body
|
| Nov 13, 2011 at 21:33 | history | edited | Daniel Moskovich | CC BY-SA 3.0 |
Fourth question added
|
| Nov 13, 2011 at 21:18 | history | asked | Daniel Moskovich | CC BY-SA 3.0 |