Noncoherence of arithmetic hyperbolic lattices

Kapovich, Michael¹

¹ Department of Mathematics, University of California, Davis, CA 95616, USA

Geometry & topology, Tome 17 (2013) no. 1, pp. 39-71.

Résumé

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.

Détail

DOI : 10.2140/gt.2013.17.39

Classification : 11F06, 20F67
Keywords: Arithmetic groups, noncoherence, example, sample layout

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