## Geometry & Topology

### Noncoherence of arithmetic hyperbolic lattices

Michael Kapovich

#### Abstract

We prove that all arithmetic lattices in $O(n,1)$, $n≥4$, $n≠7$, 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.

#### Article information

Source
Geom. Topol., Volume 17, Number 1 (2013), 39-71.

Dates
Revised: 2 September 2012
Accepted: 12 July 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732517

Digital Object Identifier
doi:10.2140/gt.2013.17.39

Mathematical Reviews number (MathSciNet)
MR3035323

Zentralblatt MATH identifier
1288.11041

#### Citation

Kapovich, Michael. Noncoherence of arithmetic hyperbolic lattices. Geom. Topol. 17 (2013), no. 1, 39--71. doi:10.2140/gt.2013.17.39. https://projecteuclid.org/euclid.gt/1513732517

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