On boundary maps of Anosov representations of a surface group to SL(3,R)
  We prove that Anosov representations from a surface group to SL(3,R) are uniquely determined by their boundary maps if and only if they do not factor over a completely reducible representation.   Furthermore we discuss representations not distinguished by their boundary maps, and we give a lower bound for the number of mapping class orbits of components of the space of Anosov representations. 
Sungwoon Kim, Thilo Kuessner
math.GT math.RT