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

Abstract

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.

33 pages, 50 figures

References in corpus (1)

• The 3D index of an ideal triangulation and angle structures

Cited by in corpus (6)

• Holography of 3d-3d correspondence at Large N
• The Ptolemy field of $3$-manifold-representations
• Complex Chern-Simons theory at level k via the 3d-3d correspondence
• A Spectral Perspective on Neumann-Zagier
• The SL(3,C)-character variety of the figure eight knot
• Ptolemy coordinates, Dehn invariant, and the A-polynomial