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The deformation spaces
of geodesic triangulations of flat tori
Yanwen Luo, Tianqi Wu and Xiaoping Zhu |
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Algebraic & Geometric Topology 24 (2024) 3605–3620
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Abstract |
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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. |
Keywords
geodesic triangulations, Tutte's embedding
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Mathematical Subject Classification
Primary: 55Q52, 57N65, 57R19, 57S05, 58D10
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References |
Publication
Received: 11 July 2021
Revised: 11 August 2023
Accepted: 17 September 2023
Published: 9 December 2024
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Authors |
| Yanwen Luo | |
| Department of Mathematics Rutgers University New Brunswick, NJ United States |
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| Tianqi Wu | |
| Center of Mathematical Sciences and
Applications Harvard University Cambridge, MA United States |
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| Xiaoping Zhu | |
| Department of Mathematics Rutgers University New Brunswick, NJ United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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