2015/10/20 by Aaron Fenyes, Fenyes, Aaron
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1510.05757
openalex publication_date 2015/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Twisted SL2 ℂ local systems on surfaces of finite type appear often in geometry and physics. Most of them arise geometrically as local systems of charts for pleated hyperbolic structures. Bonahon and Thurston's "shear-bend coordinates" parameterize these local systems of charts. On a surface with punctures, Gaiotto, Hollands, Moore and Neitzke's "abelianization" process computes the shear-bend coordinates of a twisted SL2 ℂ local system without reference to its hyperbolic geometry. Using tools from dynamics, we'll generalize abelianization to compact surfaces, leading to a dynamical recipe for the shear-bend parameterization. This recipe lends itself well to numerical approximation, and it may clarify the changes of coordinates that relate different shear parameterizations.