2015/10/20 by Aaron Fenyes, Fenyes, Aaron · 3 citations
Chemistry · Computer Science · Mathematics · #Chemistry #Composite material #Computational Geometry and Mesh Generation #Dynamical systems theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometry #Materials science #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Mathematics and Applications #Perspective (graphical) #Physics #Pure mathematics #Quantum mechanics #Recipe #Shear (geology) #math.GT
paper · pdf · doi:10.48550/arxiv.1510.05757
published in arXiv (Cornell University) (Cornell University) · 100 pages, 37 figures. v2: added secondary result (theorem 1.2.B); greatly simplified main argument, strengthening main result (theorem 1.2.A); cut material which is no longer needed (but still available in reference [1]); corrected argument in section 8.3.1 (conclusion unaffected); slightly corrected review in section 3.2.3
openalex publication_date 2015/10/20 · arxiv created 2018/08/30 · arxiv updated 2018/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
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.