Timeline for Judging whether a finitely presented group is a 3-manifold group?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2021 at 12:25 | history | edited | Stefan Kohl♦ |
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| Aug 30, 2021 at 12:25 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Oct 25, 2012 at 22:08 | answer | added | Stefan Friedl | timeline score: 8 | |
| Oct 22, 2012 at 10:08 | vote | accept | Li Yu | ||
| Oct 22, 2012 at 9:38 | answer | added | HJRW | timeline score: 15 | |
| Oct 22, 2012 at 9:38 | comment | added | HJRW | It seems to me that this question is asking for a list, and hence should be community wiki. | |
| Oct 22, 2012 at 4:15 | answer | added | Ryan Budney | timeline score: 6 | |
| Oct 22, 2012 at 3:13 | comment | added | Ryan Budney | The word problem is solved for 3-manifold groups, so whatever conditions you'd have to check, they'd be non-computable in practice. | |
| Oct 22, 2012 at 3:10 | comment | added | Li Yu | I know it is difficult to use them in practice. But I just want to know some such kind of conditions. | |
| Oct 22, 2012 at 3:00 | comment | added | Misha | @Li: There are way too many restrictions: Coherence, virtual cohomological dimension $\le 3$, every infinite amenable subgroup is polyciclic; either virtually $PD(3)$ or (virtually) splits as a free product; either contains $Z^2$ or is hyperbolic; either finite or has virtually infinite abelianization, etc. You may want to narrow down the scope of the algebraic properties you are interested in. As Igor said, most of these properties are hard (or impossible) to verify algorithmically. | |
| Oct 22, 2012 at 2:49 | comment | added | Igor Rivin | How do you tell whether a finitely presented group is residually finite? It is hard enough to tell if it is trivial... | |
| Oct 22, 2012 at 2:38 | history | asked | Li Yu | CC BY-SA 3.0 |