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math.GT2026
On Intersection of Character Varieties Associated to Dehn Fillings of the Whitehead Link and Its Generalization
Jiayu Wan, Charles Katerba
The canonical component of the character variety of a hyperbolic 2-bridge link complement M is an algebraic surface, from the work of Thurston. If we fix a boundary component T of…
math.GT2018
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…
math.GT2018
Modules, fields of definition, and the Culler-Shalen norm
Charles Katerba
Culler-Shalen theory uses the algebraic geometry of the SL(2,C)-character variety of a 3-manifold to construct essential surfaces in the manifold. There are module structures assoc…