Timeline for Is any interesting question about a group G decidable from a presentation of G?
Current License: CC BY-SA 2.5
6 events
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| Feb 23, 2010 at 14:18 | comment | added | Chad Groft |
Fair point. Actually I don't think we know anything about $\pi_2(\Sigma_k)$ in general, let alone the relative $\pi_2$ of a presentation complex for $\pi_1(\Sigma_k)$.
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| Feb 23, 2010 at 5:51 | comment | added | HJRW | Chad, I think the problem with that idea is that we need to know about $\pi_2$ of a presentation complex, not $\pi_2$ of some space with the right $\pi_1$. | |
| Feb 23, 2010 at 5:35 | comment | added | HJRW | Gah. It's gone again. | |
| Feb 23, 2010 at 3:47 | comment | added | Chad Groft | I'll check these references out in the near future. (I'm not "affiliated with an institution" at the moment, so it'll take a little while.) I know it's possible to get an effective sequence {Sigma_k} of homology n-spheres (for fixed n ≥ 5) for which the set { k : Sigma_k = S^n } is noncomputable. (Since a simply connected homology n-sphere is just the n-sphere, the set is r.e.) Also the fundamental groups would necessarily have zero homology in dimensions 1 and 2. Might it be possible to take Q_k = pi_1(Sigma_k)? What kind of control do we get on pi_2(Q_k)? | |
| Feb 23, 2010 at 3:22 | history | edited | François G. Dorais | CC BY-SA 2.5 |
fixed latex for jsmath
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| Feb 23, 2010 at 2:21 | history | answered | HJRW | CC BY-SA 2.5 |