Timeline for Which quotients of surface groups are linear?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 4, 2020 at 16:28 | comment | added | YCor | Surface group map onto $F_2$ (clear)... | |
| Mar 4, 2020 at 14:58 | comment | added | HJRW | Dani Wise has a very sophisticated result for building linear quotients of surface (and other) groups, called the malnormal special quotient theorem. If you want a very refined linear quotient of a surface group, you may want to look it up. | |
| Mar 4, 2020 at 14:42 | comment | added | Igor Belegradek | Surface groups are torsion free (except for the projective plane). | |
| Mar 4, 2020 at 14:40 | comment | added | Pat | That's amazing. Thank you. I knew this was to much to hope for. However, if the kernel is finite, I presume the answer is positive. Or is that also false? | |
| Mar 4, 2020 at 14:39 | comment | added | Igor Belegradek | Hyperbolic surface groups are SQ universal, see en.wikipedia.org/wiki/SQ-universal_group, that is every countable group embeds into their quotient. Thus just take your favorite nonlinear group and embed it in a quotient of a surface group. | |
| Mar 4, 2020 at 14:28 | history | asked | Pat | CC BY-SA 4.0 |