Density of the SO(3) TQFT representation of mapping class groups
  We show that for an odd prime r > 3 and an integer g > 1, in the projective representation given by the SO(3) Witten-Chern-Simons theory at an rth root of unity, the image of the mapping class group of a surface of genus g is dense. 
Michael Larsen, Zhenghan Wang