Figure-eight knot group and Bianchi groups admit one-parameter families of strongly parabolic-preserving deformations into SU(3,1), and infinitely many cusped hyperbolic n-manifolds have such deformations for any n >= 3.
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Parabolic-preserving deformations of cusped hyperbolic lattices
Figure-eight knot group and Bianchi groups admit one-parameter families of strongly parabolic-preserving deformations into SU(3,1), and infinitely many cusped hyperbolic n-manifolds have such deformations for any n >= 3.