Timeline for Is there a non-Hopfian lacunary hyperbolic group?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 20, 2016 at 5:41 | comment | added | HJRW | @YCor, yes. Obviously the proof must use the definition. | |
| Jun 19, 2016 at 16:51 | comment | added | YCor | I had a look at the Coulon-Guirardel paper. Before using that hyperbolic groups are hopfian, it shows (Corollary 3.5) that endomorphisms can be lifted to the free group and factor to endomorphisms of the hyperbolic groups in the approximating family. The latter point fails for arbitrary forward limits of hyperbolic groups as in my example. | |
| Jun 19, 2016 at 14:12 | comment | added | HJRW | @YCor, I was really referring to Mark Sapir's answer, although one might also conjecture (incorrectly) from the conjunction of Denis Osin's proof that lacunary hyperbolic groups are generic in limits of hyperbolic groups and your example of a non-Hopfian limit that there should be a non-Hopfian lacunary hyperbolic group. But I didn't mean to imply that you had actually made that conjecture. | |
| Jun 19, 2016 at 9:13 | comment | added | YCor | That's very nice! (But in my answer there was no claim or suggestion that I expected a positive answer.) | |
| Jun 16, 2016 at 10:37 | vote | accept | HJRW | ||
| Jun 16, 2016 at 10:37 | history | answered | HJRW | CC BY-SA 3.0 |