Timeline for Does every $SL_2\mathbb{C}$ representation of a closed oriented surface extend over a compact oriented three-manifold?
Current License: CC BY-SA 4.0
11 events
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| Feb 24, 2020 at 20:29 | answer | added | Ian Agol | timeline score: 4 | |
| Feb 24, 2020 at 0:59 | answer | added | Arun Debray | timeline score: 12 | |
| Feb 23, 2020 at 17:41 | comment | added | Danny Ruberman | Hi Charlie--It seems to me that you are asking if there are non-trivial classes in $H_2(BG^\delta)$, or perhaps how to detect such classes. You might like to have a look at Milnor's paper, On the homology of Lie groups made discrete. He cites an argument in a paper of Alperin-Dennis (due to Mather) for the case of G=SL(2,R) that might be relevant. | |
| Feb 23, 2020 at 14:26 | vote | accept | Charlie Frohman | ||
| Feb 23, 2020 at 14:21 | answer | added | Moishe Kohan | timeline score: 16 | |
| Feb 23, 2020 at 13:48 | history | edited | Charlie Frohman | CC BY-SA 4.0 |
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| Feb 23, 2020 at 13:42 | history | edited | Charlie Frohman | CC BY-SA 4.0 |
edited the question to respond to the comment.
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| Feb 23, 2020 at 12:57 | history | edited | Charlie Frohman | CC BY-SA 4.0 |
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| Feb 23, 2020 at 12:40 | history | edited | Charlie Frohman | CC BY-SA 4.0 |
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| Feb 23, 2020 at 12:36 | comment | added | Moishe Kohan | This is unlikely. The expected dimension of $X(M)$ is half of the dimension of $X(F)$, where $X$ stands for the character variety. Since there are only countably many compact 3-manifolds $M$, "most" points of $X(F)$ probably not come from restrictions. | |
| Feb 23, 2020 at 12:28 | history | asked | Charlie Frohman | CC BY-SA 4.0 |