Timeline for Mapping class groups of a punctured surface vs. surface with boundary
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2013 at 17:09 | comment | added | Anonymous | I see the problem now, thank you very much! | |
| Oct 15, 2013 at 16:24 | vote | accept | Anonymous | ||
| Oct 15, 2013 at 16:21 | comment | added | Andy Putman | @yanglee : For your first question, see any standard source on the mapping class group (eg Farb-Margalit). For your second question, try to write down a careful construction of your inclusion and you will see that it is not well-defined even though it is well-defined on Dehn twists. | |
| Oct 15, 2013 at 13:19 | comment | added | Anonymous | I am sorry, but there a still a couple of things I still don't get. I'll write here, there may be naive mistakes, please correct me if I am wrong. $PMCG(S_g^b)$ is generated by Dehn twists around non-trivial simple closed curves, right? Every non-trivial simple closed of $S_g^b$ can be seen as a non-trivial simple closed curve in $S_{g,b}$, so it seems that $PMCG(S_g^b)$ is "naturally" a subgroup of $PMCG(S_{g,b})$. So why does the inclusion $PMCG(S_{g}^b) \to PMCG(S_{g,b})$ not split the sequence above? Thank you in advance. | |
| Oct 15, 2013 at 13:18 | comment | added | Anonymous | Thank you for your answer. Could you clarify your point about abelianizations and precise why the abelianization of $PMCG(S_{g,b})$ is trivial? | |
| Oct 15, 2013 at 3:29 | history | edited | Andy Putman | CC BY-SA 3.0 |
added 28 characters in body
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| Oct 15, 2013 at 3:22 | history | answered | Andy Putman | CC BY-SA 3.0 |