Timeline for Circle bundles over $RP^2$
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Feb 20, 2022 at 19:55 | answer | added | Ian Gershon Teixeira | timeline score: 2 | |
| S Nov 3, 2015 at 7:25 | history | suggested | Ali Taghavi |
I add a tag
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| Nov 3, 2015 at 6:59 | review | Suggested edits | |||
| S Nov 3, 2015 at 7:25 | |||||
| Dec 2, 2009 at 23:51 | comment | added | Charles Rezk | To summarize Scott vs. Jason: for Scott, "circle bundle" means S^1 is the structure group, while for Jason, "circle bundle" means S^1 is the fiber. | |
| Nov 30, 2009 at 16:34 | answer | added | janmarqz | timeline score: 4 | |
| Nov 23, 2009 at 12:56 | vote | accept | Fernando Galaz-García | ||
| Nov 19, 2009 at 19:00 | comment | added | Jason DeVito - on hiatus | There are nonprincipal, nontrivial circle bundles. For example, the Klein bottle is an S^1 bundle over S^1 which is not principal and nontrivial. To see it's not principal, notice that principal circle bundles over S^1 are classified by homotopy classes of maps from S^1 into CP^\infty, but CP^\infty is 1-connected. Thus, the only principal S^1 bundle over S^1 is the trivial one, and hence the Klein bottle is NOT principal. | |
| Nov 19, 2009 at 18:27 | comment | added | S. Carnahan♦ | I apologize if I'm missing something: how do you get a circle bundle that's not principal? Do you mean "trivial" rather than "principal"? | |
| Nov 19, 2009 at 18:17 | answer | added | HJRW | timeline score: 6 | |
| Nov 19, 2009 at 18:13 | answer | added | Danny Calegari | timeline score: 18 | |
| Nov 19, 2009 at 18:01 | history | asked | Fernando Galaz-García | CC BY-SA 2.5 |