2017/09/11 by Zhe Sun, Sun, Zhe, Anna Wienhard +3
Engineering · #53C10 #Advanced Numerical Methods in Computational Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Fluid Dynamics and Vibration Analysis #Geometric Topology (math.GT) #Tribology and Lubrication Engineering
paper · pdf · doi:10.48550/arxiv.1709.03580
openalex publication_date 2017/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we define new flows on the Hitchin components for PGL(V). Special examples of these flows are associated to simple closed curves on the surface and give generalized twist flows. Other examples, so called eruption flows, are associated to pair of pants in S and capture new phenomena which are not present in the case when n = 2. Using these flows, we construct a global coordinate system on the Hitchin component. In a companion paper to this article two of the authors develop new tools to compute the Goldman symplectic form on the Hitchin component, and prove that this global coordinate system is a Darboux coordinate system.