Timeline for When are biautomatic groups hyperbolic?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2021 at 17:55 | history | edited | HJRW | CC BY-SA 4.0 |
Minor edits
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| Nov 11, 2021 at 16:43 | vote | accept | Ross Griebenow | ||
| Nov 11, 2021 at 15:00 | comment | added | YCor | Yes, this is the simple observation I had in mind. For some reason it seemed to be unnoticed by several people. | |
| Nov 11, 2021 at 14:46 | comment | added | HJRW | @YCor: it's easy to see: $BS(m,n)$ is an HNN extension of the torus-link group $\mathbb{Z}*_{m=n}\mathbb{Z}$, and one can see this has a $\mathbb{Z}^2$ subgroup in various ways. For instance, the fact that it's the torus-link group proves it immediately geometrically, or one can construct the embedding explicitly. I don't know a reference, though, if that's what you're asking for. | |
| Nov 11, 2021 at 10:47 | comment | added | YCor | I'm curious where the fact that $\mathrm{BS}(2,3)$ possesses a $\mathbf{Z}^2$ subgroup can be located. When I was PhD I asked whether it holds to a few people and at least two "famous" people proved me shaking hands that it doesn't. But it indeed does contain such a $\mathbf{Z}^2$ subgroup (as does $\mathrm{BS}(m,n)$ whenever $\min(|m|,|n|)\ge 2$), and this is not hard to check. I'm asking it here because it's implicit in passing the question from $\mathrm{BS}(m,n)$ subgroups (as it appears in Bestvina's list) to $\mathrm{BS}(1,n\ge 1)$ subgroups that the other cases are actually redundant. | |
| Nov 11, 2021 at 10:41 | history | edited | YCor | CC BY-SA 4.0 |
replaced ill-formated --, fixed BS
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| Nov 11, 2021 at 8:37 | history | answered | HJRW | CC BY-SA 4.0 |