CMSA Interdisciplinary Science Seminar: The deformation space of geodesic triangulations and Tutte’s embedding
Tianqi Wu - CMSA
In 1984, Bloch, Connelly, and Henderson proved that the space of geodesic triangulations of a convex polygon is contractible. It was found that Tutte’s embedding theorem could give a very simple proof to Bloch-Connelly-Henderson’s theorem, and provides an elegant algorithm for image morphing on convex polygons. We recently generalize Tutte’s embedding theorem, and prove that the deformation space of geodesic triangulations of a closed Riemannian surface of negative curvature is contractible. This confirms a conjecture by Connelly, Henderson, Ho, Starbird in 1983, and also indicates a method for image morphing on closed surfaces.