Timeline for Positive genus Fuchsian groups
Current License: CC BY-SA 4.0
11 events
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| Sep 6, 2020 at 17:33 | vote | accept | user163814 | ||
| Aug 18, 2020 at 16:47 | history | edited | Moishe Kohan | CC BY-SA 4.0 |
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| Aug 18, 2020 at 16:39 | history | edited | Moishe Kohan | CC BY-SA 4.0 |
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| Aug 18, 2020 at 16:32 | history | edited | Moishe Kohan | CC BY-SA 4.0 |
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| Aug 18, 2020 at 16:22 | history | edited | Moishe Kohan | CC BY-SA 4.0 |
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| Aug 16, 2020 at 19:01 | comment | added | Moishe Kohan | @YCor: After some group-theoretic work, yes, but Siegel says nothing of sorts. It's possible that he was unaware of the result. | |
| Aug 16, 2020 at 18:18 | comment | added | YCor | But probably the Poincaré/Siegel argument yields the whole result (not only finite generation)? | |
| Aug 16, 2020 at 18:10 | history | edited | Moishe Kohan | CC BY-SA 4.0 |
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| Aug 16, 2020 at 18:09 | comment | added | Moishe Kohan | @YCor: I meant discrete subgroups. As for finite generation of lattices in $PSL(2,R)$, it was known much earlier than the general case, the earliest reference I know is in Siegel's 1945 Annals paper "Some remarks on discontinuous groups." He even gives a bound on the number of generators in terms of area. Siegel's argument is by looking closely at fundamental polygons, it is likely that his proof goes back to Poincare. | |
| Aug 16, 2020 at 17:45 | comment | added | YCor | I don't think the case of finitely generated subgroups of $(P)SL(2,\mathbf{R})$ is any easier than the general case, or even known before. However, for finitely generated discrete subgroups it's possibly an earlier result. Another issue is that it's not a trivial fact that lattices are finitely generated (it's trivial for cocompact lattices), but finite generation of arbitrary lattices is the main issue. | |
| Aug 16, 2020 at 17:28 | history | answered | Moishe Kohan | CC BY-SA 4.0 |