Timeline for morphism from a compact group to Z ?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 19, 2014 at 11:07 | comment | added | Sean Eberhard | This is a nice lemma. The heart of the matter seems to be in proving that a compact connected group is divisible, which uses a little structure theory. Once you know this then you know that any map $G\to\mathbf{Z}$ factors through the profinite group $G/G_0$, and then by the universal property of profinite completion you need only check there is no nontrivial homomorphism $\widehat{\mathbf{Z}}\to\mathbf{Z}$, which is straightforward. | |
| Nov 17, 2011 at 7:49 | vote | accept | Florent MARTIN | ||
| Nov 17, 2011 at 7:49 | |||||
| Nov 15, 2011 at 12:45 | history | edited | Alain Valette | CC BY-SA 3.0 |
added 52 characters in body; deleted 19 characters in body
|
| Nov 15, 2011 at 12:33 | history | answered | Alain Valette | CC BY-SA 3.0 |