Duality and invariants of representations of fundamental groups of   3-manifolds into PGL(3,C)
  We determine the explicit transformation under duality of generic configurations of four flags in $\PGL(3,\bC)$ in cross-ratio coordinates. As an application we prove invariance under duality of an invariant in the Bloch group obtained from decorated triangulations of 3-manifolds. 
Elisha Falbel, Qingxue Wang
math.GT