Timeline for Relationship between étale and topological $K(\pi,1)$s
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 26, 2015 at 16:22 | comment | added | Donu Arapura | Yes, I believe 2 and 3 are still open. Serre, in one of his books, asked explicitly whether the Higman group occurs as the fundamental group of a smooth projective variety. If so, it would provide a counterexample to 2. I'm not aware of any progress on this. | |
| Jul 26, 2015 at 14:54 | comment | added | Alex Youcis | Thanks for the nice explicit example Donu! By the way, you mentioned above that you thought that 2,3 were open. Do you still believe that? I haven't been able to find any explicit answers online, but that doesn't mean much. There is the book 'Fundamental Groups of Compact Kahler Manifolds', but I don't feel like reading hundreds of pages, and can't find a super relevant proposition. Thanks again! | |
| Jul 26, 2015 at 12:16 | history | edited | Donu Arapura | CC BY-SA 3.0 |
added 323 characters in body
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| Jul 26, 2015 at 11:37 | comment | added | Donu Arapura | The point of going to level $\ge 3$ is that $\Gamma(n)$ acts without fixed points, so you can use the usual $\pi_1$. | |
| Jul 26, 2015 at 9:31 | comment | added | Piotr Achinger | I think you need to use the orbifold fundamental group of the moduli space (fundamental group of the stack), correct? | |
| Jul 25, 2015 at 15:53 | history | answered | Donu Arapura | CC BY-SA 3.0 |