Timeline for Does every mapping class group embed into some $\mathrm{Out}(F_n)$?
Current License: CC BY-SA 4.0
9 events
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| Nov 15 at 16:15 | comment | added | Matt Zaremsky | Ah OK, so I guess not so helpful for higher genus, since braid groups embedding in $\mathrm{Out}(F_n)$ is "old news". | |
| Nov 15 at 14:32 | comment | added | Ian Agol | The centralizer of a hyperelliptic, quotient the hyperelliptic, is a mapping class group of a $2g+2$ pointed sphere. So essentially a braid group. | |
| Nov 15 at 14:26 | comment | added | Matt Zaremsky | That's a nice argument for $g=2$! I suppose maybe this same argument shows that for any genus, the centralizer of the hyperelliptic involution embeds in $\mathrm{Mod}(S_{2g+2,g})$ and hence in $\mathrm{Out}(F_{4g+1})$? But I don't really have a sense of how "big" these centralizers are when $g>2$, or whether that should count as "evidence" for the main question. | |
| Nov 15 at 11:05 | history | edited | YCor | CC BY-SA 4.0 |
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| Nov 15 at 6:06 | history | edited | Ian Agol | CC BY-SA 4.0 |
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| Nov 15 at 5:34 | history | undeleted | Ian Agol | ||
| Nov 15 at 5:34 | history | edited | Ian Agol | CC BY-SA 4.0 |
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| Nov 15 at 5:32 | history | deleted | Ian Agol | via Vote | |
| Nov 15 at 5:29 | history | answered | Ian Agol | CC BY-SA 4.0 |