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Gluing equations for real projective structures on 3-manifolds
Samuel A. Ballas, Alex Casella
Given an orientable ideally triangulated --manifold , we define a system of real valued equations and inequalities whose solutions can be used to construct projective structu…
Branched Cauchy-Riemann Structures on Once-Punctured Torus Bundles
Alex Casella
Unlike in hyperbolic geometry, the monodromy ideal triangulation of a hyperbolic once-punctured torus bundle has no natural geometric realisation in Cauchy-Riemann (CR) space…
Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3-manifolds
Alex Casella, Charles Katerba, Stephan Tillmann
Closed essential surfaces in a three-manifold can be detected by ideal points of the character variety or by algebraic non-integral representations. We give examples of closed esse…
Moduli spaces of real projective structures on surfaces: Notes on a paper by V.V. Fock and A.B. Goncharov
Alex Casella, Dominic Tate, Stephan Tillmann
These notes grew out of our learning and applying the methods of Fock and Goncharov concerning moduli spaces of real projective structures on surfaces with ideal triangulations. We…