## Geometry & Topology

### Kleinian groups and the rank problem

#### Abstract

We prove that the rank problem is decidable in the class of torsion-free word-hyperbolic Kleinian groups. We also show that every group in this class has only finitely many Nielsen equivalence classes of generating sets of a given cardinality.

#### Article information

Source
Geom. Topol., Volume 9, Number 1 (2005), 375-402.

Dates
Accepted: 28 February 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799570

Digital Object Identifier
doi:10.2140/gt.2005.9.375

Mathematical Reviews number (MathSciNet)
MR2140986

Zentralblatt MATH identifier
1087.20035

#### Citation

Kapovich, Ilya; Weidmann, Richard. Kleinian groups and the rank problem. Geom. Topol. 9 (2005), no. 1, 375--402. doi:10.2140/gt.2005.9.375. https://projecteuclid.org/euclid.gt/1513799570

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