The Deformation Space of Geodesic Triangulations and Generalized Tuttes Embedding Theorem

We proved the contractibility of the deformation space of the geodesic triangulations on a closed surface of negative curvature. This solves an open problem proposed by Connelly et al. in 1983, in the case of hyperbolic surfaces. The main part of the proof is a generalization of Tuttes embedding theorem for closed surfaces of negative curvature.