Residually finite non linear hyperbolic groups

TL;DR

This paper constructs the first known examples of residually finite, non-linear Gromov hyperbolic groups using amalgamated products of specific lattices in rank 1 Lie groups, advancing understanding in geometric group theory.

Contribution

It provides the first explicit examples of residually finite, non-linear hyperbolic groups, constructed via amalgamation of lattices in Lie groups.

Findings

First examples of residually finite non-linear hyperbolic groups.

Construction method using amalgamated products of lattices.

Advances understanding of hyperbolic group structures.

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.