Kleinian groups and the rank problem

Kapovich, Ilya¹ ; Weidmann, Richard²

¹ Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801, USA
² Fachbereich Mathematik, Johann Wolfgang Goethe Universität, Robert Mayer-Straße 6–8, 60325 Frankfurt, Germany

Geometry & topology, Tome 9 (2005) no. 1, pp. 375-402.

Résumé

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.

Détail

DOI : 10.2140/gt.2005.9.375

Keywords: word-hyperbolic groups, Nielsen methods, 3–manifolds

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