Timeline for Finite models for torsion-free lattices
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2020 at 13:01 | comment | added | Moishe Kohan | @YCor No, I do not. One can go through Gromov's argument and check if it can be modified to deal with orbifolds. My guess is that it works. Gelander, I think, would be the person to ask since he improved Gromov's proof. | |
| Feb 19, 2020 at 10:35 | comment | added | YCor | Do you know if there's a statement covering both results? Namely in the same setting but applying to possibly non-torsion-free lattices? | |
| Feb 19, 2020 at 9:08 | comment | added | Moishe Kohan | @StefanWitzel That I do not know, Gromov's argument is differential-geometric. | |
| Feb 19, 2020 at 9:06 | comment | added | Moishe Kohan | @H1ghfiv3 There are many arguments, for instance, use an equivariant isometric embedding in the symmetric space of $SL(n, R)$, which would have to be real analytic. Or use the fact that the metric on the symmetric space is obtained by applying action of it's isometry group (which is real analytic) to a K- invariant metric on the tangent soace at the point corresponding to K in G/K. | |
| Feb 19, 2020 at 8:00 | comment | added | Stefan Witzel | @MoisheKohan Neat! You don't happen to know of any generalization to other lattices in locally compact CAT(0)-groups (like algebraic groups over local fields)? I'm asking because in certain cases there is an answer similar to the one I sketched, but it uses heavy machinery (reduction theory) and it is an open problem to understand how much of that one could do purely geometrically. | |
| Feb 19, 2020 at 7:52 | comment | added | Stefan Witzel | @H1ghfiv3 I think this will come from the fact that your groups are real points of algebraic groups. | |
| Feb 19, 2020 at 7:42 | comment | added | H1ghfiv3 | Just one question: Do they also show that locally symmetric spaces of non-positive curvature are analytic ? | |
| Feb 19, 2020 at 7:35 | vote | accept | H1ghfiv3 | ||
| Feb 19, 2020 at 1:29 | history | answered | Moishe Kohan | CC BY-SA 4.0 |