Congruence RFRS towers
Annales de l'Institut Fourier, Online first, 27 p.

We describe a criterion for a real or complex hyperbolic lattice to admit a residually finite rational solvable (RFRS) tower that consists entirely of congruence subgroups. We use this to show that certain Bianchi groups PSL 2 (𝒪 d ) are virtually fibered on congruence subgroups, and also exhibit the first examples of RFRS Kähler groups that are not a subgroup of a product of surface groups and abelian groups.

Nous donnons un critère pour qu’un réseau réel ou complexe hyperbolique admette une tour résiduellement finie rationnelle soluble (RFRS) qui se compose entièrement de sous-groupes de congruence. Nous l’utilisons pour montrer que certains groupes de Bianchi PSL 2 (𝒪 d ) sont virtuellement fibrés sur des sous-groupes de congruence, et donnons aussi les premiers exemples de groupes de Kähler RFSR qui ne sont pas des sous-groupes d’un produit de groupes de surface et de groupes abéliens.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3532
Classification: 20H10,  22E40,  11F06,  20H05,  32Q15,  57K32
Keywords: RFRS towers, Bianchi groups, congruence subgroups, real and complex hyperbolic lattices, virtual fibering, Kähler groups.
Agol, Ian 1; Stover, Matthew 2

1 University of California Berkeley, Berkeley, CA (USA)
2 Temple University, Philadelphia, PA (USA)
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Agol, Ian; Stover, Matthew. Congruence RFRS towers. Annales de l'Institut Fourier, Online first, 27 p.

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