Noncoherence of arithmetic hyperbolic lattices

Kapovich, Michael

doi:10.2140/gt.2013.17.39

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Noncoherence of arithmetic hyperbolic lattices

Michael Kapovich

Geometry & Topology 17 (2013) 39–71

DOI: 10.2140/gt.2013.17.39

Abstract

We prove that all arithmetic lattices in $O (n, 1)$ , $n \geq 4$ , $n \neq 7$ , are noncoherent. We also establish noncoherence of uniform arithmetic lattices of the simplest type in $SU (n, 1)$ , $n \geq 2$ , 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

Volume 17, issue 1 (2013)