Timeline for Geometry and topology of Fuchsian character varieties
Current License: CC BY-SA 4.0
15 events
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| Dec 6 at 0:32 | history | edited | user82261 | CC BY-SA 4.0 |
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| Dec 5 at 23:21 | answer | added | Moishe Kohan | timeline score: 2 | |
| Dec 5 at 22:45 | comment | added | HJRW | @MoisheKohan: well I think that’s the answer to the first part of the question! | |
| Dec 5 at 17:41 | comment | added | Moishe Kohan | @HJRW Smoothness for representations to Lie groups was known for general Fuchsian groups for 20 years before Goldman and is due to Andre Weil. (One only needs the coadjiont representation to have no nonzero fixed vectors.) | |
| Dec 5 at 12:57 | comment | added | user82261 | @HJRW That's one way to put it, lol. I wonder, though, if anything is already known about $SU(n)$-Fuchsian character varieties. Perhaps not (correct me if I am wrong), I guess, but I thought it was worth a shot asking here. | |
| Dec 5 at 12:15 | comment | added | HJRW | It's perfectly natural to wonder whether the work of Goldman, Magee etc can be generalised from surfaces to arbitrary Fuchsian groups. You could try combing through the 355 (!) papers on MathSciNet that cite Goldman's article. You could also try contacting Magee directly. | |
| Dec 4 at 14:50 | history | edited | HJRW |
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| Dec 4 at 14:50 | history | edited | user82261 | CC BY-SA 4.0 |
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| Dec 4 at 14:49 | comment | added | user82261 | @HJRW Ah, I see. I'll remove that comment then. | |
| Dec 4 at 14:48 | comment | added | HJRW | You say you're interested in the co-compact case. Perhaps it's worth pointing out that, in this case, the torsion-free case that you ask about at the end is precisely the case of a surface group $\Sigma_g$. | |
| Dec 4 at 14:43 | comment | added | user82261 | Corrected typos and added information about definition of a Fuchsian group. | |
| Dec 4 at 14:42 | history | edited | user82261 | CC BY-SA 4.0 |
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| Dec 4 at 14:40 | comment | added | Moishe Kohan | You should start by defining what exactly do you mean by a Fuchsian (not Fucschian) group. Specifically, do you only consider subgroups of $PSL(2,\mathbb R)$ or allow orientation-reversing isometries as well. And you are misstating the definition of a character variety. | |
| Dec 4 at 13:39 | history | edited | user82261 | CC BY-SA 4.0 |
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| Dec 4 at 13:17 | history | asked | user82261 | CC BY-SA 4.0 |