Volume 17, issue 1 (2013)

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Noncoherence of arithmetic hyperbolic lattices

Michael Kapovich

Geometry & Topology 17 (2013) 39–71
Abstract

We prove that all arithmetic lattices in O(n,1), n 4, n7, are noncoherent. We also establish noncoherence of uniform arithmetic lattices of the simplest type in SU(n,1), n 2, and of uniform lattices in SU(2,1) which have infinite abelianization.

Keywords
Arithmetic groups, noncoherence, example, sample layout
Mathematical Subject Classification 2010
Primary: 11F06
Secondary: 20F67
References
Publication
Received: 7 September 2011
Revised: 2 September 2012
Accepted: 12 July 2012
Published: 14 February 2013
Proposed: Martin Bridson
Seconded: Walter Neumann, Leonid Polterovich
Authors
Michael Kapovich
Department of Mathematics
University of California
Davis, CA 95616
USA
http://www.math.ucdavis.edu/~kapovich