Timeline for Judging whether a finitely presented group is a 3-manifold group?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2021 at 12:25 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Jan 10, 2016 at 10:49 | comment | added | Sam Nead | Thinking about homology considerations tells us that the longitude of X is glued to the longitude of Y - that reduces the set of possible gluings to a "line" of Dehn twists. I think that your "challenge" could now be answered computationally if we had a facility to glue manifolds with torus boundary. Does that exist? | |
| Jan 10, 2016 at 10:15 | comment | added | Sam Nead | If I haven't made a mistake: I used a variety of tools, ending with snappy, to obtain a triangulation of this three-manifold M. I then used regina to find fundamental normal tori. Cutting proves that M is obtained by gluing X, the figure eight knot complement, to Y, the Seifert fibered space with base orbifold D(2,2) (aka the orientation I-bundle over the Klein bottle). Unfortunately, regina doesn't track gluing data when we cut along a normal torus. So we can't recover the gluing data that way. | |
| Oct 26, 2012 at 4:54 | comment | added | Sam Nead | The program Heegaard (written by Berge) says the presentation is realizable. So yes, it is a three-manifold group. Also, the homology is Z. If pressed I would take the diagram that his program produces, convert that to a triangulation, and feed the result to SnapPy. | |
| Oct 22, 2012 at 4:15 | history | answered | Ryan Budney | CC BY-SA 3.0 |