Timeline for Is there a contractible hyperbolic 3-orbifold of finite volume?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2022 at 21:59 | comment | added | Sam Nead | @MoisheKohan - could I ask you (pretty please!) to (try to) avoid "biting the hyperbolic geometry newbies"? Thank you! | |
| Nov 28, 2022 at 18:49 | comment | added | ThiKu | @Moishe Kohan: Most people think of hyperbolic space as a concrete model, say upper half space or disk model. The notation as a homogeneous space is then just a short way to define it. | |
| Nov 28, 2022 at 16:04 | answer | added | IJL | timeline score: 6 | |
| Nov 28, 2022 at 14:15 | comment | added | David.D | It is true that I am not very familiar with hyperbolic geometry. I copied the above description from wikipedia without checking. The version I am interested in is $\operatorname{SO}^\circ(3,1)/\operatorname{SO}(3)$ where $\operatorname{SO}^\circ(3,1)$ is the connected component that contains the identity. | |
| Nov 28, 2022 at 13:54 | comment | added | Moishe Kohan | It does not seem like you know the actual definition because what's written now is not even wrong but meaningless. If you want to describe $H^3$ as a quotient of a simple Lie group by its maximal compact subgroup, you should first decide if you consider orientation-preserving or all isometries. In the former case, you could use $PSL(2,C)/SO(3)$, in the latter case you could use $PO(3,1)/PO(3)$. | |
| Nov 28, 2022 at 12:20 | comment | added | ThiKu | Well, now O(3) is not a subgroup of SO(3,1). But we all know, what is meant. | |
| Nov 28, 2022 at 10:40 | history | edited | David.D | CC BY-SA 4.0 |
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| Nov 28, 2022 at 10:19 | comment | added | David.D | You are right! I have edited the question again. | |
| Nov 28, 2022 at 10:17 | history | edited | David.D | CC BY-SA 4.0 |
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| Nov 28, 2022 at 10:12 | comment | added | Moishe Kohan | Well, it is still wrong, with your new definition $H^3$ has two connected components! | |
| Nov 28, 2022 at 8:29 | history | edited | YCor |
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| Nov 28, 2022 at 7:50 | comment | added | David.D | It is a typo. I have edited the questions. | |
| Nov 28, 2022 at 7:45 | history | edited | David.D | CC BY-SA 4.0 |
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| Nov 28, 2022 at 6:39 | comment | added | ThiKu | I guess it’s a typo. SO(3) in place of SO(1) will be fine. | |
| Nov 28, 2022 at 4:23 | history | became hot network question | |||
| Nov 28, 2022 at 1:30 | comment | added | Moishe Kohan | Your definition of the hyperbolic 3-space is plain wrong. | |
| Nov 27, 2022 at 21:22 | vote | accept | David.D | ||
| Nov 27, 2022 at 21:06 | answer | added | Sam Nead | timeline score: 15 | |
| Nov 27, 2022 at 20:22 | history | asked | David.D | CC BY-SA 4.0 |