Geodesic
The deformation spaces of geodesic triangulations of flat tori
Luo, Yanwen1 ; Wu, Tianqi2 ; Zhu, Xiaoping1
1 Department of Mathematics, Rutgers University, New Brunswick, NJ, United States
2 Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 7, pp. 3605-3620

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2024.24.3605
Keywords: geodesic triangulations, Tutte's embedding

Luo, Yanwen 1 ; Wu, Tianqi 2 ; Zhu, Xiaoping 1

1 Department of Mathematics, Rutgers University, New Brunswick, NJ, United States
2 Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA, United States 
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Luo, Yanwen; Wu, Tianqi; Zhu, Xiaoping. The deformation spaces of geodesic triangulations of flat tori. Algebraic and Geometric Topology, Tome 24 (2024) no. 7, pp. 3605-3620. doi: 10.2140/agt.2024.24.3605

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