Timeline for Do surface groups embed into PSL_2 over a real quadratic integer ring?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2021 at 23:32 | vote | accept | Ian Gershon Teixeira | ||
| Dec 15, 2021 at 19:04 | history | edited | Ian Gershon Teixeira | CC BY-SA 4.0 |
added 592 characters in body; edited title
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| Dec 15, 2021 at 8:22 | answer | added | Jean Raimbault | timeline score: 4 | |
| Dec 14, 2021 at 13:33 | history | edited | Ian Gershon Teixeira | CC BY-SA 4.0 |
added 26 characters in body
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| Dec 14, 2021 at 13:14 | history | edited | Ian Gershon Teixeira | CC BY-SA 4.0 |
edited title
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| Dec 14, 2021 at 7:33 | answer | added | Jean Raimbault | timeline score: 4 | |
| Dec 14, 2021 at 4:36 | comment | added | Ian Gershon Teixeira | @JeanRaimbault My mistake the question contains an incorrect assertion as asked. I'll change it from $ \mathbb{Q} $ to $ \mathbb{Z} $ | |
| Dec 14, 2021 at 4:26 | history | edited | Ian Gershon Teixeira | CC BY-SA 4.0 |
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| Dec 13, 2021 at 7:52 | comment | added | Jean Raimbault | if I remember it correctly Takeuchi's proof is essentially algorithmic ; you take any representation, then you find rational matrices which are close to the images of the generators and satisfy the surface group relation, and you conclude by applying the Calabi--Weil rigidity theorem which tells you that this gives a faithful discrete representation. | |
| Dec 13, 2021 at 7:46 | comment | added | Jean Raimbault | Indeed representations with $\mathbb Q$-coefficients are dense in the set of $\mathrm{PSL}_2(\mathbb R)$-representations for a surface group, this is due to Takeuchi (zbmath.org/?q=an%3A0204.39801) ; a generalisation to Fuchsian groups with torsion is given by Maclachlan and Waterman (zbmath.org/?q=an%3A0552.20028). | |
| Dec 11, 2021 at 23:11 | comment | added | Moishe Kohan | BTW, degree 2 fields are easy to find, but my guess is that one can also do this rationally. | |
| Dec 11, 2021 at 20:36 | comment | added | Moishe Kohan | How do you prove the claim about PSL(2,Q)? | |
| Dec 11, 2021 at 19:22 | comment | added | Will Sawin | A solution for $g=2$ gives a solution for every other $g$ by taking covering spaces. | |
| Dec 11, 2021 at 19:01 | history | edited | LSpice | CC BY-SA 4.0 |
a -> an
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| Dec 11, 2021 at 15:35 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Dec 11, 2021 at 15:11 | history | asked | Ian Gershon Teixeira | CC BY-SA 4.0 |