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Kleinian groups and the rank problem

Ilya Kapovich and Richard Weidmann

Geometry & Topology 9 (2005) 375–402

DOI: 10.2140/gt.2005.9.375

arXiv: math.GT/0407438
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
Mathematical Subject Classification

Primary: 20F67, 57M60

Secondary: 30F40
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Publication

Received: 31 August 2004
Accepted: 28 February 2005
Published: 3 March 2005
Proposed: Walter Neumann
Seconded: Wolfgang Metzler, Cameron Gordon
Authors
Ilya Kapovich
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 West Green Street
Urbana
Illinois 61801
USA
Richard Weidmann
Fachbereich Mathematik
Johann Wolfgang Goethe Universität
Robert Mayer-Straß e 6–8
60325 Frankfurt
Germany