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

Yanwen Luo, Tianqi Wu and Xiaoping Zhu

Geometry & Topology 27 (2023) 3361–3385
Abstract

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
Mathematical Subject Classification
Primary: 54C25, 55Q52, 57N65, 57S05, 58D10
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
Authors
Yanwen Luo
Department of Mathematics
Rutgers University
New Brunswick, NJ
United States
Tianqi Wu
Center of Mathematical Sciences and Applications
Harvard University
Cambridge, MA
United States
Xiaoping Zhu
Department of Mathematics
Rutgers University
New Brunswick, NJ
United States

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