Timeline for Example of three dimensional atoroidal Poincaré duality group with some pathology
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 22, 2023 at 13:54 | comment | added | HJRW | A small remark. The word "atoroidal" has two different meanings in 3-manifold topology: no essential embedded torus and no essential "immersed" torus. Examples that are atoroidal in the first sense are easier to write down (although not necessarily hyperbolic): you can use Brieskorn spheres, Seifert-fibred spaces fibring over hyperbolic triangle orbifolds. | |
| Dec 22, 2023 at 13:47 | comment | added | HJRW | Can I suggest replacing "some pathology" in the title with "Property FA"? It's just as short and completely precise! | |
| Dec 17, 2023 at 17:22 | vote | accept | Peter Kropholler | ||
| Dec 16, 2023 at 23:18 | history | became hot network question | |||
| Dec 16, 2023 at 21:07 | answer | added | Sam Nead | timeline score: 12 | |
| Dec 16, 2023 at 18:15 | comment | added | Peter Kropholler | @AGenevois yes that is right: an explicit example of a non-Haken hyprbolic closed 3-manifold would answer my question. So a natural question arises: is the Seifert--Weber dodecahedral space Haken. | |
| Dec 16, 2023 at 16:13 | comment | added | AGenevois | In arxiv:2312.08913, it is mentioned that a theorem of Stallings shows that, given a closed, orientable, aspherical 3-manifold $M$, $\pi_1(M)$ has property FA iff $M$ is non-Haken. So it seems that your question amounts to finding explicit examples of non-Haken hyperbolic closed 3-manifolds. | |
| Dec 16, 2023 at 15:18 | history | asked | Peter Kropholler | CC BY-SA 4.0 |