Freely indecomposable groups acting on hyperbolic spaces

Details Freely indecomposable groups acting on hyperbolic spaces Freely indecomposable groups acting on hyperbolic spaces

2002-03-02

arxiv.org/abs/math/0203015v2

Mathematics

Group Theory

to appear in Intern. J. Algebra and Comput

Scientific paper

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 $G$.

Affiliated with

Also associated with

No associations

Rating

Freely indecomposable groups acting on hyperbolic spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Freely indecomposable groups acting on hyperbolic spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Freely indecomposable groups acting on hyperbolic spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-645777