The symplectic properties of the PGL($n,\mathbb{C}$)-gluing equations

Abstract

In [12] we studied PGL($n,\mathbb{C}$)-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 similar symplectic properties of the PGL($n,\mathbb{C}$)-gluing equations for all ideal triangulations of compact oriented 3-manifolds.