Timeline for Embedded 2-tori in $S^1\times S^4$
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 6, 2023 at 20:28 | answer | added | Ian Agol | timeline score: 7 | |
| Sep 3, 2023 at 13:54 | comment | added | Dmitrii Ivanov | @ Danny Rubermann and Marco Golla, yes, that's what I meant. | |
| Sep 3, 2023 at 13:53 | history | edited | Dmitrii Ivanov | CC BY-SA 4.0 |
deleted 1 character in body
|
| Sep 3, 2023 at 11:41 | comment | added | Neil Strickland | If we regard $T$ as $\{(z,w)\in\mathbb{C}^2:|z|=|w|=1\}$ and $S^4$ as $\mathbb{C}^2\cup\{\infty\}$ then for $n\in\mathbb{Z}$ we can define $f_n(z,w)=(z^n,(z,w))$; these are all different homotopy classes. | |
| Sep 3, 2023 at 11:40 | comment | added | Marco Golla | So maybe the question should be "does homotopy imply isotopy for 2-tori in $S^1\times S^4$?". | |
| Sep 3, 2023 at 11:24 | comment | added | Danny Ruberman | To expand a bit on @Marco's comment, you presumably mean isotopy where you wrote homotopy. | |
| Sep 3, 2023 at 7:42 | comment | added | Marco Golla | There are 2-tori that are not null-homotopic: the map induced on $pi_1$ can be trivial (e.g. "local" tori) or non-trivial (e.g. the product $S^1\times S^1 \subset S^1\times S^4$). | |
| S Sep 2, 2023 at 21:21 | review | First questions | |||
| Sep 2, 2023 at 21:31 | |||||
| S Sep 2, 2023 at 21:21 | history | asked | Dmitrii Ivanov | CC BY-SA 4.0 |