Timeline for Freedom problem in hyperbolic groups
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 2, 2020 at 15:12 | comment | added | HJRW | You might like to compare with Question 9.4 of arxiv.org/abs/1003.5117 . Bridson and I asked if the finite presentation problem is (uniformly) solvable over hyperbolic groups. If the freedom problem is unsolvable in some hyperbolic group, then the answer to our question is (as expected) "no". | |
| Jan 2, 2020 at 13:52 | comment | added | Misha | @YCor: Yes, of course; ditto for infinite simple groups, groups containing $Z^2$, etc., which is why I assumed that $G$ is free, so we have an ample supply of homomorphisms. | |
| Jan 2, 2020 at 9:35 | comment | added | YCor | BTW if $H$ is hyperbolic and $G$ is a f.p. group with non-solvable word problem, the question of injectivity for homomorphisms $G\to H$ is quite easy to solve :) | |
| Jan 2, 2020 at 4:07 | history | became hot network question | |||
| Jan 1, 2020 at 23:09 | answer | added | YCor | timeline score: 4 | |
| Jan 1, 2020 at 20:34 | comment | added | Derek Holt | This question seems to be about a special case of your general question. I seem to remember asking Martin Bridson about the decidability of the freeness (freedom?) of subgroups of hyperbolic groups, and I believe that he thought that it was unknown but likely to be undecidable. | |
| Jan 1, 2020 at 20:13 | history | edited | Misha | CC BY-SA 4.0 |
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| Jan 1, 2020 at 19:59 | history | asked | Misha | CC BY-SA 4.0 |