Timeline for Are fundamental groups of aspherical manifolds Hopfian?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20, 2010 at 17:28 | answer | added | Ian Agol | timeline score: 12 | |
| Apr 13, 2010 at 22:21 | vote | accept | Sergei Ivanov | ||
| Apr 9, 2010 at 17:28 | comment | added | HJRW | One partial result: if a closed manifold X admits a metric of negative sectional curvature bounded away from 0 then it follows from a theorem of Sela that $\pi_1(X)$ is Hopfian. | |
| Apr 9, 2010 at 17:10 | answer | added | Igor Belegradek | timeline score: 9 | |
| Apr 9, 2010 at 16:55 | comment | added | HJRW | I suspect that the closest known such group is the example of a non-Hopfian CAT(0) group that Wise constructed in his thesis. | |
| Apr 9, 2010 at 16:44 | comment | added | Igor Belegradek | I think the question "do closed aspherical manifolds have Hopfian fundamental group?" is a well-known open problem. The difficulty in Question 2 is that non-Hopfian finitely presented groups are not so easy to construct; it is a good question! | |
| Apr 9, 2010 at 12:33 | comment | added | Sergei Ivanov | I'm interested in higher homology groups. | |
| Apr 9, 2010 at 12:30 | comment | added | Paul | For question 2, $f$ induces an epi on abelianizations, i.e. on $H_1(G;Z)$. The universal coefficient theorem shows it remains epi over $Z/2$ or $Q$. | |
| Apr 9, 2010 at 12:29 | answer | added | Tom Church | timeline score: 20 | |
| Apr 9, 2010 at 12:16 | history | asked | Sergei Ivanov | CC BY-SA 2.5 |