Timeline for Defining a map into $S^1$ as an "angle" in a non simply connected domain
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2021 at 20:04 | vote | accept | username | ||
| Mar 26, 2021 at 20:04 | vote | accept | username | ||
| Mar 26, 2021 at 20:04 | |||||
| Mar 12, 2021 at 15:05 | vote | accept | username | ||
| Mar 26, 2021 at 20:04 | |||||
| Mar 12, 2021 at 9:37 | answer | added | Thomas Rot | timeline score: 2 | |
| Mar 12, 2021 at 9:09 | history | edited | username | CC BY-SA 4.0 |
deleted 79 characters in body; edited title
|
| Mar 12, 2021 at 8:57 | history | edited | username | CC BY-SA 4.0 |
deleted 79 characters in body; edited title
|
| S Mar 10, 2021 at 20:00 | history | bounty ended | CommunityBot | ||
| S Mar 10, 2021 at 20:00 | history | notice removed | CommunityBot | ||
| S Mar 2, 2021 at 18:13 | history | bounty started | username | ||
| S Mar 2, 2021 at 18:13 | history | notice added | username | Authoritative reference needed | |
| Mar 1, 2021 at 21:09 | history | edited | username | CC BY-SA 4.0 |
deleted 388 characters in body; edited title
|
| Feb 22, 2021 at 9:26 | comment | added | username | @KevinCasto I meant in the case when the domain isn't simply connected | |
| Feb 14, 2021 at 4:09 | comment | added | Kevin Casto | Then the claim is true -- any continuous map from a simply connected space to $S^1$ is null-homotopic and therefore lifts to a map to $\mathbb R$. This is just basic algebraic topology, at least in the continuous category. I'm sure it's straightforward to extend this result to $W^{1,p}$. | |
| Feb 13, 2021 at 17:25 | comment | added | username | @KevinCasto thank you yes, probably. What happens in that case though? | |
| Feb 12, 2021 at 21:43 | history | edited | username | CC BY-SA 4.0 |
added 392 characters in body; edited tags
|
| Feb 12, 2021 at 15:29 | comment | added | Kevin Casto | Perhaps further up in the text they have specified that $\Omega$ is simply connected? Otherwise you run into the issue you mention. | |
| Feb 12, 2021 at 15:18 | history | edited | username | CC BY-SA 4.0 |
added 54 characters in body
|
| Feb 12, 2021 at 14:33 | history | asked | username | CC BY-SA 4.0 |