Timeline for Motivation of the fundamental theorem of covering spaces
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 2, 2022 at 15:36 | comment | added | user483320 | Thank you very much! | |
| Jun 2, 2022 at 15:33 | comment | added | Maxime Ramzi | @user483320 : yes, exactly ! And by covering theory, the category of $\pi_1(S^1)$-sets is equivalent to the category of covers of $S^1$, which is something you can access geometrically (for instance by finding the universal cover, $\mathbb R$, or by using $S^1= [0,1]/(0=1)$ | |
| Jun 2, 2022 at 15:29 | comment | added | user483320 | How do you calculate $\pi_1(S^1)$ using the fundamental theorem of covering spaces? If by "the knowledge that you can recover π1 from the category of π1-sets" you mean that whenever G-set and H-set are equivalent categories, then G is isomorphic to H -- so can we calculate $\pi_1(S^1)$ by proving that the category of $\pi_1(S^1)$-sets is equivalent to the category of $\mathbb Z$-sets, is that what you are saying? | |
| May 9, 2022 at 18:11 | history | answered | Maxime Ramzi | CC BY-SA 4.0 |