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 $O\left(n,1\right)$, $n\ge 4$, $n\ne 7$, are noncoherent. We also establish noncoherence of uniform arithmetic lattices of the simplest type in $\mathit{SU}\left(n,1\right)$, $n\ge 2$, and of uniform lattices in $\mathit{SU}\left(2,1\right)$ which have infinite abelianization.

Keywords
Arithmetic groups, noncoherence, example, sample layout
Primary: 11F06
Secondary: 20F67
Publication
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