Gluing equations for real projective structures on 3-manifolds

Abstract

Given an orientable ideally triangulated 3-manifold M, we define a system of real valued equations and inequalities whose solutions can be used to construct projective structures on M. These equations represent a unifying framework for the classical Thurston gluing equations in hyperbolic geometry and their more recent counterparts in Anti-de Sitter and halfpipe geometry. Moreover, these equations can be used to detect properly convex structures on M. The paper also includes explicit examples where the equations are used to construct properly convex structures.