Timeline for Extension of isotopies
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 30, 2023 at 16:09 | comment | added | Ryan Budney | As long as there is sufficient smoothness and your subset has a regular neighbourhood, the basic proof of isotopy extension works. Perhaps take a look at the proof in Hirsch's Differential Topology textbook. It will give you an idea of ways the application can be generalized. | |
| Nov 30, 2023 at 16:05 | history | edited | Tommaso Rossi | CC BY-SA 4.0 |
added 141 characters in body
|
| Nov 30, 2023 at 15:42 | comment | added | Tommaso Rossi | Thanks @IgorBelegradek, I think I get your point, I will look at the Goresky-MacPherson book! | |
| Nov 30, 2023 at 15:38 | comment | added | Igor Belegradek | The definition of normal crossing that I know involves smoothness: en.wikipedia.org/wiki/…. The paper you linked to contains references to Stratified Morse theory and other works on the subject, so hopefully you can find a reference there. | |
| Nov 30, 2023 at 15:06 | comment | added | Tommaso Rossi | Sorry, in what sense the normal crossing setting is smooth? A normal crossing divisor is not a manifold (unless there are no crossings) so I think the only definition of isotopy that make sense is the one of Kirby-Edwards...am I wrong? Anyway, thanks for the reference, I will look at it! | |
| Nov 30, 2023 at 14:37 | comment | added | Igor Belegradek | Are you asking for topological isotopies or smooth ones? The normal crossing setting is smooth, while Edwards-Kirby setting is topological. Did you check "Stratified Morse theory" by Gorseky-MacPherson? | |
| Nov 30, 2023 at 12:04 | history | asked | Tommaso Rossi | CC BY-SA 4.0 |