Timeline for A group, all of whose non-trivial mapping tori are finitely presentable?
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8 events
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| Sep 13, 2023 at 23:31 | comment | added | Matt Zaremsky | I'd say another "candidate" comes from Thompson's group $F$. Let $\phi:F\to\mathbb{Z}$ send $f$ to the log base 2 of the slope of $f$ at 0 plus the log base 2 of the slope of $f$ at 1. Then the kernel of $\phi$ is finitely generated but not finitely presented. I wouldn't be surprised if all the non-trivial mapping tori of this kernel are isomorphic to $F$, or really close. And $F$ has lots of automorphisms, so if this turned out to work, it would be "interesting". | |
| Sep 13, 2023 at 15:49 | comment | added | YCor | The non-fp group $\mathbf{Z}\ltimes (\mathbf{Z}[1/2]^2)$, action by diagonal $(2,2^{-1})$ might be more interesting to look at. Of course one can cheat and act by a virtually inner automorphism (e.g., flip of components). But otherwise any "non-inner enough" automorphism is likely to produce a fp group. | |
| Sep 13, 2023 at 15:43 | comment | added | YCor | @Carl-FredrikNybergBrodda No, it doesn't have any. | |
| Sep 13, 2023 at 14:50 | comment | added | Moishe Kohan | As a toy model one can ask the same question about nontrivial mapping tori which are all finitely generated. Does it imply finite generation of the original group? | |
| Sep 13, 2023 at 13:23 | comment | added | Benjamin Steinberg | You might look at the comments to mathoverflow.net/questions/104400/… | |
| Sep 13, 2023 at 11:01 | comment | added | Carl-Fredrik Nyberg Brodda | What happens for the lamplighter group? Does it have any finitely presented mapping torus? | |
| Sep 13, 2023 at 10:37 | history | edited | ADL | CC BY-SA 4.0 |
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| Sep 13, 2023 at 10:32 | history | asked | ADL | CC BY-SA 4.0 |