Let $G$ be a real Lie group and $\Gamma < G$ be a discrete subgroup of $G$. Is $\Gamma$ residually finite? This paper describes known positive and negative results then poses some questions whose answers will lead to a fairly complete answer for lattices.
Residual finiteness of certain 2-dimensional Artin groups
On the residual finiteness of outer automorphisms of relatively hyperbolic groups
The residual finiteness of (hyperbolic) automorphism-induced HNN-extensions
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