Timeline for Jordan Curve Homotopy
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 21, 2010 at 4:52 | vote | accept | Sergeib | ||
| Jul 21, 2010 at 4:17 | answer | added | Tom Goodwillie | timeline score: 10 | |
| Jul 21, 2010 at 3:43 | answer | added | Kerry | timeline score: 0 | |
| Jul 21, 2010 at 2:57 | answer | added | Andy Putman | timeline score: 4 | |
| Jul 21, 2010 at 2:45 | comment | added | Mariano Suárez-Álvarez | Louis H. Kauffman gives a cute proof in his Knots and physics for smooth curves. | |
| Jul 21, 2010 at 2:41 | comment | added | Andy Putman | It always exists if the orientations of C_0 and C_1 match up. First, homotope C_0 so C_1 lies in the precompact region of R^2-C_0 ("blow it up" -- you can achieve this using affine transformations). Using the Schönflies theorem, you can then deduce that C_0 and C_1 bound an embedded annulus in the plane, which you can then use as a guide to homotope C_0 to C_1. | |
| Jul 21, 2010 at 2:33 | comment | added | Mariano Suárez-Álvarez | The orientation of $C_0$ and of $C_1$ should match for such an homotopy to exist, at the very least. | |
| Jul 21, 2010 at 2:29 | history | asked | Sergeib | CC BY-SA 2.5 |