The Deformation Spaces of Geodesic Triangulations of Flat Tori

Yanwen Luo; Tianqi Wu; Xiaoping Zhu

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arXiv · 2107.05159

The Deformation Spaces of Geodesic Triangulations of Flat Tori

Yanwen Luo·Tianqi Wu·Xiaoping Zhu

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Abstract

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.

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Yanwen Luo, Tianqi Wu, Xiaoping Zhu. 2021-07-12. The Deformation Spaces of Geodesic Triangulations of Flat Tori. https://arxiv.org/abs/2107.05159

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