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The
deformation space of geodesic triangulations and generalized
Tutte's embedding theorem
Yanwen Luo, Tianqi Wu and Xiaoping Zhu |
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Geometry & Topology 27 (2023) 3361–3385
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Abstract |
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We prove the contractibility of the deformation space of the geodesic triangulations on a closed surface of negative curvature. This solves an open problem, proposed by Connelly, Henderson, Ho and Starbird (1983), in the case of hyperbolic surfaces. The main part of the proof is a generalization of Tutte’s embedding theorem for closed surfaces of negative curvature. |
Keywords
geodesic triangulations, Tutte's embedding
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Mathematical Subject Classification
Primary: 54C25, 55Q52, 57N65, 57S05, 58D10
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References |
Publication
Received: 18 July 2021
Revised: 16 January 2022
Accepted: 18 February 2022
Published: 9 November 2023
Proposed: Benson Farb
Seconded: David Fisher, Mladen Bestvina
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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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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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