The deformation space of geodesic triangulations and generalized Tutte’s embedding theorem

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

Geometry & topology, Tome 27 (2023) no. 8, pp. 3361-3385.

Résumé

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.

Détail

DOI : 10.2140/gt.2023.27.3361

Keywords: geodesic triangulations, Tutte's embedding

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