Timeline for Fundamental groups of $\mathcal{M}_{0,n}$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 26, 2016 at 16:33 | comment | added | Dan Petersen | The fundamental group of the moduli space $M_{g,n}$ is the mapping class group of a genus $g$ surface with $n$ punctures. So you are asking about the mapping class group of an $n$ times punctured sphere. It is related both to the usual pure braid group and to the spherical braid group. | |
| Sep 26, 2016 at 14:39 | vote | accept | stupid_question_bot | ||
| Sep 26, 2016 at 9:44 | answer | added | S. Carnahan♦ | timeline score: 7 | |
| Sep 26, 2016 at 3:26 | comment | added | stupid_question_bot | @HeinrichD Sure, I suppose, but I'm only asking about the algebraically closed, characteristic 0 case, so I don't think there's much of a difference. | |
| Sep 26, 2016 at 0:31 | comment | added | HeinrichD | Do you actually mean the profinite completion of $F_2$? | |
| Sep 25, 2016 at 23:14 | comment | added | HJRW | One description is given by the Birman exact sequence, which says the kernel of the forget-a-strand map is free. | |
| Sep 25, 2016 at 23:12 | comment | added | HJRW | The ordered versions are the pure braid groups. | |
| Sep 25, 2016 at 23:03 | comment | added | Will Chen | @JesseSilliman I believe the braid groups are fundamental groups of the moduli stacks with $n$ unordered points. For example, $F_2$ is not a braid group. | |
| Sep 25, 2016 at 23:01 | comment | added | Jesse Silliman | I think they are n-stranded braid groups. | |
| Sep 25, 2016 at 22:42 | history | asked | stupid_question_bot | CC BY-SA 3.0 |