Timeline for Restriction of diffeomorphisms homotopic to identity to the boundary
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2020 at 4:16 | vote | accept | Cusp | ||
| May 11, 2020 at 0:23 | answer | added | Moishe Kohan | timeline score: 4 | |
| May 9, 2020 at 4:23 | comment | added | Moishe Kohan | Path component of the identity means isotopy. To get 1, just restrict the isotopy to the boundary, it remains isotopy. (The difference with homotopy is that boundary maps to boundary.) To get 2, use the existence of a collar neighborhood of the boundary which is the product $\partial M\times [0,1]$. | |
| May 9, 2020 at 4:19 | comment | added | Cusp | Good point. The paper states simply the "path component of identity". Also even for isotopy the first one is straightforward but how to prove the second one? Any reference for that. | |
| May 9, 2020 at 4:16 | comment | added | Moishe Kohan | Both claims hold (with easy proofds) if you replace homotopy with isotopy; are you sure they use homotopy in the paper? The restriction map does not (in general, send diffeomorphisms homotopic to the identity to diffeomorphisms homotopic to the identity. | |
| May 9, 2020 at 3:23 | history | asked | Cusp | CC BY-SA 4.0 |