Geometry & Topology, Vol. 9 (2005) Paper no. 12, pages 375--402.

Kleinian groups and the rank problem

Ilya Kapovich, Richard Weidmann

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.

Keywords. Word-hyperbolic groups, Nielsen methods, 3-manifolds

AMS subject classification. Primary: 20F67, 57M60. Secondary: 30F40.

DOI: 10.2140/gt.2005.9.375

E-print: arXiv:math.GT/0407438

Submitted to GT on 31 August 2004. Paper accepted 28 February 2005. Paper published 3 March 2005.

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Ilya Kapovich, Richard Weidmann
Department of Mathematics, University of Illinois at Urbana-Champaign
1409 West Green Street, Urbana, IL 61801, USA
and
Fachbereich Mathematik, Johann Wolfgang Goethe Universitat
Robert Mayer-Strasse 6-8, 60325 Frankfurt, Germany

Email: kapovich@math.uiuc.edu, rweidman@math.uni-frankfurt.de

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