Fundamental groups of non-compact arithmetic hyperbolic n-manifolds (n≥4) contain thin surface subgroups; doubles of cusped ones embed as GFERF subgroups of SO^+(n+1,1).
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The double of a virtually compact special Gromov-hyperbolic group along a quasiconvex subgroup is virtually compact special, with a generalization to certain graphs of groups.
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Thin surface subgroups of non-uniform arithmetic lattices in $\rm{SO}^+(n,1)$
Fundamental groups of non-compact arithmetic hyperbolic n-manifolds (n≥4) contain thin surface subgroups; doubles of cusped ones embed as GFERF subgroups of SO^+(n+1,1).