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Noncoherence of some lattices in Isom(Hn)

Michael Kapovich, Leonid Potyagailo and Ernest Vinberg

Geometry & Topology Monographs 14 (2008) 335–351

DOI: 10.2140/gtm.2008.14.335

arXiv: math/0608415
Abstract

We prove noncoherence of certain families of lattices in the isometry group of the hyperbolic n–space for n greater than 3. For instance, every nonuniform arithmetic lattice in SO(n,1) is noncoherent, provided that n is at least 6.

To the memory of Heiner Zieschang
Keywords

coherence, hyperbolic space, lattices
Mathematical Subject Classification

Primary: 22E40

Secondary: 20F65
References
Publication

Received: 14 August 2006
Accepted: 18 November 2006
Published: 29 April 2008
Authors
Michael Kapovich
Department of Mathematics
University of California, Davis
1 Shields Ave
CA 95616
USA
Leonid Potyagailo
UFR de Mathématiques
Université de Lille 1
59655 Villeneuve d'Ascq cedex
France
Ernest Vinberg
Department of Mechanics and Mathematics
Lomonosov Moscow State University
Vorob'evy Gory
Moscow 119992, GSP-2
Russia