Strongly Dense Representations of Hyperbolic 3-Manifold Groups

We provide the first examples of strongly dense representations of a hyperbolic 3-manifold group into $SL(4,\mathbb{R})$ and $SU(3,1)$ i.e. representations where every pair of non-commuting elements has Zariski dense image. Our examples are holonomy representations arising from projective deformations of its hyperbolic structure. As a Corollary, we get that $SL(4,\mathbb{R})$ has non-Hitchin strongly dense surface subgroups.