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Residually finite non linear hyperbolic groups

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arxiv 2207.14356 v1 pith:XHFEF2PA submitted 2022-07-28 math.GR

Nicolas Tholozan , Konstantinos Tsouvalas This is my paper · ORCID
classification math.GR
keywords examplesfinitegroupshyperbolicresiduallyalongamalgamatedcocompact
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abstract

We exhibit the first examples of residually finite non-linear Gromov hyperbolic groups. Our examples are constructed as amalgamated products of torsion-free cocompact lattices in the rank 1 Lie group $\mathrm{Sp}(d,1)$, $d\geq 2$ along maximal cyclic subgroups.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Residual Finiteness Growth in Two-Step Nilpotent Groups

    math.GR 2025-05 conditional novelty 7.0 of 10

    For two-step nilpotent groups, residual finiteness growth is at most log^{d+1}, with d an invariant of the complex Mal'cev completion, and is exactly log^{d+1} when the commutator subgroup has rank at most 2.

  2. Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio

    math.GT 2026-07 accept novelty 6.5 of 10

    For every n≥3 there are infinitely many pairwise incommensurable finite-volume hyperbolic n-manifolds with totally geodesic boundary sharing one fixed perimeter-to-volume ratio.

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