Timeline for Amalgmated free product of hyperbolic groups with one malnormal and one virtual factor is hyperbolic?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 24, 2013 at 22:45 | vote | accept | K. Bulinski | ||
| Aug 24, 2013 at 18:14 | comment | added | HJRW | Here's the abstract page for Misha's link: arxiv.org/abs/math/9605205 . (In general, I prefer not to have to download a whole pdf file just to see what the link is.) | |
| Aug 24, 2013 at 16:53 | comment | added | Misha | See also theorem 2 in arxiv.org/pdf/math/9605205v1.pdf | |
| Aug 24, 2013 at 16:08 | answer | added | HJRW | timeline score: 4 | |
| Aug 24, 2013 at 15:30 | comment | added | Misha | Instead of "One" I should have said "Bestvina and Feighn". Another remark is that, currently, there are no examples of f.g. subgroups of hyperbolic groups which are malnormal and not quasiconvex. See mathoverflow.net/questions/134091 . However, one can prove existence of infinite rank free malnormal subgroups in every nonelementary hyperbolic group. Taking a double along such subgroup, leads to a group which is not finitely presentable and, hence, not hyperbolic. | |
| Aug 24, 2013 at 15:11 | comment | added | Misha | You (and your source) are misstating combination theorem: One has to assume in addition that $H$ is quasiconvex in both $G_1, G_2$, while malnormality in, fact, can be weakened to a "flaring condition" (you should read the original paper instead). Once you realize this, you see that malnormality in one of the subgroups is sufficient (but not necessary), since it implies "2-acylindricity" of the action on the tree, which, in turn, implies flaring. | |
| Aug 24, 2013 at 15:05 | history | asked | K. Bulinski | CC BY-SA 3.0 |