Timeline for Conjugate Groups of (quasi) Fuchsian Groups
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2010 at 18:00 | comment | added | BrainDead | Not at all. I haven't been able to find what I need in Gardiner, but I can probably prove (or disprove) your statement. The group multiplication as far as I know is only right continuous (holomorphic) for $T(1)$, but not left continuous. (Lehto has a very clean example of this using piecewise linear functions in his book.) | |
| Dec 3, 2010 at 14:44 | comment | added | Autumn Kent | Sorry about all of my silly comments this morning, you can ignore all my previous comments (I'm a little doped up on cold medicine). You were right about the definition of Teichmuller trivial. I do think the answer that I have up now should be the correct one, and you should be able to derive it from the cases you mentioned. I do know that $\mathrm{Teich}(1)$ is a group as you say, but you have to be careful about the order of composition, or else the group law isn't continuous. I'm not sure about the more general situation. I can try and dig up a reference if you like. | |
| Dec 3, 2010 at 14:21 | comment | added | BrainDead | Sorry, perhaps my question was a bit round-about. What I'm really interested in getting out of this question is whether there are appropriate normalizations on the solutions so that $T(\Gamma)$ becomes an honest group from composition of the solutions. I imagine this is not going to be possible in general. | |
| Dec 3, 2010 at 13:56 | history | edited | Autumn Kent | CC BY-SA 2.5 |
deleted 54 characters in body
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| Dec 3, 2010 at 13:51 | history | edited | Autumn Kent | CC BY-SA 2.5 |
Changed condition.
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| Dec 3, 2010 at 13:41 | comment | added | Autumn Kent | Sorry, by "these" I meant the maps whose boundary values agree with a Mobius transformation. | |
| Dec 3, 2010 at 13:39 | comment | added | Autumn Kent | Yes, but the normalized solutions for these are the identity on $\mathbb{R}$. Maybe I don't have the right terminology for the differentials in the infinite covolume case, but that should be the correct condition. | |
| Dec 3, 2010 at 13:34 | comment | added | BrainDead | Aren't "Teichmuller trivial" differentials those solutions whose restriction to a real line is that of an element in $PSL(2,\mathbb{R})$? | |
| Dec 3, 2010 at 3:57 | history | edited | Autumn Kent | CC BY-SA 2.5 |
rewording
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| Dec 3, 2010 at 3:47 | history | answered | Autumn Kent | CC BY-SA 2.5 |