English

The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem

Geometric Topology 2023-11-22 v1 Differential Geometry

Abstract

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 Tutte's embedding theorem for closed surfaces of negative curvature.

Keywords

Cite

@article{arxiv.2105.00612,
  title  = {The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem},
  author = {Yanwen Luo and Tianqi Wu and Xiaoping Zhu},
  journal= {arXiv preprint arXiv:2105.00612},
  year   = {2023}
}

Comments

18 pages, 5 figures. Comments are welcomed!