Freely indecomposable groups acting on hyperbolic spaces
| dc.creator | Kapovich, Ilya | |
| dc.creator | Weidmann, Richard | |
| dc.date | 2002-03-02 | |
| dc.date | 2002-10-19 | |
| dc.date.accessioned | 2026-07-07T04:46:47Z | |
| dc.date.available | 2026-07-07T04:46:47Z | |
| dc.description | We obtain a number of finiteness results for groups acting on Gromov-hyperbolic spaces. In particular we show that a torsion-free locally quasiconvex hyperbolic group has only finitely many conjugacy classes of $n$-generated one-ended subgroups. We also show that the rank problem is solvable for the class of torsion-free locally quasiconvex hyperbolic groups (even though it is unsolvable for the class of all torsion-free hyperbolic groups). We apply our results to 3-manifold groups. Namely, suppose $G$ is the fundamental group of a closed hyperbolic 3-manifold fibering over a circle and suppose that all finitely generated subgroups of $G$ are topologically tame. We prove that for any $k\ge 2$ the group $G$ has only finitely many conjugacy classes of non-elementary freely indecomposable $k$-generated subgroups of infinite index in $G$. | |
| dc.description | to appear in Intern. J. Algebra and Comput | |
| dc.identifier | https://arxiv.org/abs/math/0203015 | |
| dc.identifier | http://arxiv.org/abs/math/0203015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63475 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F67 | |
| dc.title | Freely indecomposable groups acting on hyperbolic spaces | |
| dc.type | text |