Kleinian groups and the rank problem

Kapovich, Ilya; Weidmann, Richard

doi:10.2140/gt.2005.9.375

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

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 2000

Primary: 20F67, 57M60

Secondary: 30F40

References

Forward citations

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

Volume 9, issue 1 (2005)