Timeline for Second Betti number of lattices in $\mathrm{SL}_3(\mathbf{R})$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 5, 2018 at 17:36 | comment | added | YCor | Steffen's method does not apply to arithmetic subgroups of $\mathrm{SL}_1(D)$, if I'm correct. So it would be interesting to check this case. Note: $\mathrm{SL}_1(D)$ is a torsion-free group (for any central cubic division algebra $D$ over $\mathbf{Q}$). | |
| Oct 29, 2018 at 15:24 | comment | added | Venkataramana | @Kionke: Sorry. Representations contributing to $H^2$ for SL(3) is indeed tempered, so my comments were wrong (and deleted). | |
| Oct 29, 2018 at 13:33 | comment | added | Steffen Kionke | @Venkataramana: I think, it is an old result of Lee-Schwermer that there is a lot of cuspidal cohomology for principal congruence subgroups of $SL_3(\mathbb{Z})$. See link.springer.com/article/10.1007%2FBF01394023 | |
| Oct 28, 2018 at 11:04 | comment | added | Aurel | @Venkataramana Thanks, that is probably why I should have checked the details... :-) There is something I don't understand in your commment : why is the representation contributing to $H^2$ not tempered? Are you saying that the $H^2_{\rm cusp}$ is trivial for congruence subgroups of ${\rm SL}_3(\mathbb{Z})$? Many examples have been computed and these cohomology spaces are non-trivial. | |
| Oct 27, 2018 at 23:12 | history | answered | Aurel | CC BY-SA 4.0 |