Timeline for What does it matter if a group has a non-elementary hyperbolic quotient?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 26, 2021 at 17:59 | vote | accept | Ethan Dlugie | ||
| Jan 22, 2021 at 13:09 | comment | added | YCor | An infinite hyperbolic quotient is an obstruction to some strong versions of Property T, including V. Lafforgue's strong property T. I don't known if these properties are known to fail for MCGs. | |
| Jan 22, 2021 at 8:31 | comment | added | HJRW | ... Regarding the "thinness" of the connection or otherwise, you are, of course, entitled to your opinion (although it doesn't carry much weight from an anonymous user), but it's irrelelant to the question, which asks for motivation to study hyperbolic quotients of mapping class groups. My answer lays out the motivation as I see it. I'd be very interested to hear anyone else's ideas. | |
| Jan 22, 2021 at 7:46 | comment | added | HJRW | @dodd: Since you don't point out where I assume hyperbolic groups are residually finite, I assume you concede that your previous comment was incorrect. On the last question we interacted on, you also made an incorrect comment and never conceded that you were wrong. This is not a good pattern of behaviour. There's no shame in being wrong. | |
| Jan 22, 2021 at 3:02 | comment | added | markvs | @HJRW: Otherwise a connection with finite quotients would be even thinner than it is now. | |
| Jan 21, 2021 at 22:16 | comment | added | HJRW | @dodd: Where...? | |
| Jan 21, 2021 at 22:14 | comment | added | markvs | @HJRW: In your answer you assume that all hyperbolic groups are residually finite. | |
| Jan 21, 2021 at 22:11 | comment | added | HJRW | @dodd: on the contrary, as I explain in my answer, there is some precedent for using non-elementary hyperbolic quotients to study finite quotients. It's certainly difficult, but these are difficult problems, | |
| Jan 21, 2021 at 22:05 | answer | added | HJRW | timeline score: 7 | |
| Jan 21, 2021 at 20:51 | comment | added | markvs | I do not think you can get anything new and particularly interesting if you know that a non-elementary hyperbolic quotient exists. You will get SQ-universality of the mapping class groups, but that already follows from acylindrical hyperbolicity: en.wikipedia.org/wiki/Acylindrically_hyperbolic_group. In particular any new results about finite quotients and profinite completion are hard to expect, | |
| Jan 21, 2021 at 19:56 | comment | added | Carl-Fredrik Nyberg Brodda | Re: separability. A subgroup of a group is separable if it is closed in the profinite topology. An easy property of a f.g. separable subgroup $H$ of a f.p. group $G$ is that one can algorithmically recognise non-membership in $H$. Since one can always recognise membership in $H$, one can thus decide membership in $H$. This problem is called the subgroup membership problem for $H$ in $G$, and is interesting in its own right. A group in which all f.g. subgroups are separable is called subgroup separable, or LERF (locally extended residually finite, note the similarity to residual finiteness). | |
| Jan 21, 2021 at 19:25 | history | edited | YCor | CC BY-SA 4.0 |
removed "et al"
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| Jan 21, 2021 at 18:24 | history | asked | Ethan Dlugie | CC BY-SA 4.0 |