Visualizing deformations of complex structures on 4-punctured spheres (Intelligence of Low-dimensional Topology)

Abstract

Once the quadratic differential (1) is obtained one may compute horizontal and vertical direction using the definition q(z)v² ∈ℝ>₀⋅and q(z)v² ∈ℝ>₀⋅. One need to be careful when one draws flow lines because quadratic differentials. Also one may generate a movie of Teichmüller geodesic as we indeed have computed geodesic axises of pseudo-Anosov mapping classes. Some movies by the author are available at https://www.youtube.com/playlist?list=PLQLzkZ9xZDXiVz-fS7EqU6RYh6L2h1wVB. Those movies take the Teichmüller distance dt into account, and hence movies are "unit-speed" with respect to dt.