Volume 9, issue 1 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Kleinian groups and the rank problem

Ilya Kapovich and Richard Weidmann

Geometry & Topology 9 (2005) 375–402

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 2000
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-Straße 6–8
60325 Frankfurt
Germany