  We study here the space of representations of a fundamental group of a
3-manifold into PGL(n,C). Thurston, Neumann and Zagier initiated a strategy (in
the case of PGL(2,C)) consisting in: triangulate the manifold, assign shapes to
each pieces and then try to glue back. This leads to the "gluing equations" and
the Neumann-Zagier symplectic space.
  Building on the works of Dimofte-Gabella-Goncharov and
Bergeron-Falbel-Guilloux, we complete the picture in the case of PGL(n,C). We
recover a situation very similar to the case of PGL(2,C). This allows for
example to obtain a combinatorial proof of a local rigidity results for such
representations.
