The symplectic properties of the PGL(n,C)-gluing equations

In a previous article we studied PGL(n,C)-representations of a 3-manifold via a generalization of Thurston's gluing equations. Neumann has proved some symplectic properties of Thurston's gluing equations that play an important role in recent developments of exact and perturbative Chern-Simons theory. In this paper, we prove the symplectic properties of the PGL(n,C)-gluing equations for all ideal triangulations of compact oriented 3-manifolds.