Work

The deformation spaces of geodesic triangulations of flat tori

Year: 2024

Type: article

Abstract: We prove that the deformation space of geodesic triangulations of a flat torus is homotopically 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.While this paper was under preparation, Erickson and Lin proved a similar result, which works for all convex drawings.55Q52, 57N65, 57R19, 57S05, 58D10Let ' be a map from T .1/ to T 2 .Assume ' maps every edge in E to a geodesic arc parametrized by Œ0; 1 with constant speed on T 2 .A positive assignment w 2

Source: Algebraic & Geometric Topology

DOI: 10.2140/agt.2024.24.3605

Authors: Yanwen Luo, Tianqi Wu, Xiaoping Zhu

Institutions: Rutgers, The State University of New Jersey, Harvard University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Awards: FRG: Collaborative Research: Geometric and Topological Methods for Analyzing Shapes, FRG: Collaborative Research: Geometric and Topological Methods for Analyzing Shapes, Discrete Conformal Geometry of Surfaces and Applications, Collaborative Research: ATD: Theory and Algorithms for Discrete Curvatures on Network Data from Human Mobility and Monitoring