Geometry & Topology

Kleinian groups and the rank problem

Ilya Kapovich and Richard Weidmann

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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

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

Received: 31 August 2004
Accepted: 28 February 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F67: Hyperbolic groups and nonpositively curved groups 57M60: Group actions in low dimensions
Secondary: 30F40: Kleinian groups [See also 20H10]

word-hyperbolic groups Nielsen methods 3–manifolds


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.

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