We show that the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the representation variety, where or , answering a question of W. M. Goldman. We also prove the existence of faithful representations into with certain nonintegral Toledo invariants.
Jason Deblois. Richard P. Kent IV. "Surface groups are frequently faithful." Duke Math. J. 131 (2) 351 - 362, 01 February 2006. https://doi.org/10.1215/S0012-7094-06-13125-3