2021/07/12 by Yanwen Luo, Luo, Yanwen, Tianqi Wu +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2107.05159
openalex publication_date 2021/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the deformation space of geodesic triangulations of a flat torus is homotopy equivalent to a torus. This solves an open problem proposed by Connelly et al. in 1983, in the case of flat tori. A key tool of the proof is a generalization of Tutte's embedding theorem for flat tori. When this paper is under preparation, Erickson and Lin proved a similar result, which works for all convex drawings.