Timeline for Borel-Serre compactification of $\mathbb{H}^3 / SL_2(\mathcal{O}_K)$
Current License: CC BY-SA 3.0
13 events
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| Jun 22, 2022 at 8:13 | history | edited | CommunityBot |
replaced http://math.uga.edu/~pete with http://alpha.math.uga.edu/~pete
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 23, 2014 at 0:07 | comment | added | jacob | @MatthiasWendt I am just confused as to what the topology looks like at the boundary, and would like to understand it better. So I'd like to understand what the open sets like. For instance, in terms of $NAM$ decomposition relative to a cusp, we add a copy of $M/(M\cap K)$ at the boundary. But then if I actually want a neighborhood of a point $m$ in there, can it be built of product sets such as $B_N\times B_M\times B_A$? If so, what do these sets look like? | |
| Aug 21, 2014 at 13:52 | comment | added | Matthias Wendt | @jacob: I do not really understand what you mean. What exactly would you like to know? (I thought about this a bit and I am not sure if I can say much about those neighbourhoods apart from the definition.) | |
| Aug 17, 2014 at 1:23 | comment | added | jacob | Would you explain what the neighborhoods of the boundary look like, please? That is, given a point $z$ on the boundary, how do describe a fundamental system of open sets around $z$? Thanks! | |
| Jul 26, 2014 at 18:06 | comment | added | Matthias Wendt | @IanAgol: thanks for your comment, sorry I forgot about the cases with exceptionally big unit group. I added some clarification discussing these cases. | |
| Jul 26, 2014 at 18:04 | comment | added | Matthias Wendt | @BenWieland: thanks for your comment, I added some clarification what I meant with the naturality comment. | |
| Jul 26, 2014 at 17:59 | history | edited | Matthias Wendt | CC BY-SA 3.0 |
added 917 characters in body
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| Jul 24, 2014 at 4:25 | comment | added | Ian Agol | There's a minor correction: for $K=\mathbb{Q}[\sqrt{-1}], \mathbb{Q}[\sqrt{-3}]$, the cusp is actually an orbifold quotient of the elliptic curve by the group of units. | |
| Jul 23, 2014 at 21:57 | comment | added | hyp93 | Mathias, thanks for this wonderful answer! | |
| Jul 23, 2014 at 21:56 | vote | accept | hyp93 | ||
| Jul 23, 2014 at 21:44 | comment | added | Ben Wieland | The complex structure is natural. The boundary of the locally symmetric space is a subquotient of the boundary of the symmetric space, from which it inherits local properties. As you said, the boundary of 3d hyperbolic space is $\mathbb C\mathbb P^1$; in general, the boundary of hyperbolic space has a unique conformal structure preserved by the group of hyperbolic isometries. | |
| Jul 23, 2014 at 20:12 | history | answered | Matthias Wendt | CC BY-SA 3.0 |